Knot Atlas - User contributions [en]

7 7 Further Notes and Views

2025-11-02T16:58:46Z

Robert FERREOL: adding new picture

<noinclude>Back to [[7 7]].</noinclude>
<br>
{|
|- valign=top
{{Knot View Template|
image = 7crossings-semiregular-inrectangle.png |
text = Ornamental knot}}

{{Knot View Template|
image = Knot77.gif |
text = Mongolian ornament ; sum of two 7.7}}

{{Knot View Template|
image = 7.7.png |
text = Depiction with three loops}}

{{Knot View Template|
image = NOEUD.jpg |
text = Sum of 4.1 and 7.7}}

{{Knot View Template|
image = Noeud 77 chinois.jpg |
text = 7.7 in calligraphy by Christoph Soland}}
|}

File:Noeud 77 chinois.jpg

2025-11-02T16:55:46Z

Robert FERREOL: Noeud 7.7 caligraphie

== Summary ==
Noeud 7.7 caligraphie

L6a3 Further Notes and Views

2024-11-21T08:52:09Z

Robert FERREOL: right link

<noinclude>Back to [[L6a3]]</noinclude><br>
{|
|- valign=top
{{Knot View Template|
image = 6a3Oberwolfach92_160.jpg |
text = Ruberman, Cochran, Melvin, Akbulut, Gompf, Kirby [https://celebratio.org/Kirby_RC/viewer/562/]}}
|
{{Knot View Template|
image = 6a3BySchwartz_120.png |
text = Rich Schwartz' "72" [http://www.math.umd.edu/~res/poster.html]}}
|
{{Knot View Template|
image = Triangle-Interlaced-Circle.gif |
text = Triangle interlaced with a circle, a traditional symbol of the Christian Trinity (less used in recent centuries) }}
|
{{Knot View Template|
image = Trefoil-Architectural-Equilateral-Triangle-interlaced.png |
text = An architectural trefoil (the outline of three overlapping circles) interlaced with an equilateral triangle, another old Christian Trinitarian symbol.}}

|
{{Knot View Template|
image = Noeud-de-cochon.png |
text = Closed granny knot.}}
|}

<div class="NavFrame"><div class="NavHead">Further images</div>
<div class="NavContent">
{| style="background: transparent;"
|- valign=top
{{Knot View Template|
image = Celtic flag proposed.png |
text = Celtic flag proposal.}}
{{Knot View Template|
image = Blonay-Vaud-Switzerland-flag.gif |
text = Flag of Blonay, Vaud, Switzerland.}}
{{Knot View Template|
image = Eye of Providence inside triangle interlaced with circle Venice.jpg |
text = "Eye of Providence" inside triangle interlaced with circle, Venice.}}
{{Knot View Template|
image = Six-circles-star-David.png |
text = Composed of intersecting circles.}}
|-
{{Knot View Template|
image = Hexagramm aus Nepal.jpg |
text = Hindu hexagram symbol with Aum/Om, from Nepal.}}
{{Knot View Template|
image = double boomerang.jpg |
text = Double boomerang-like Kolam and Linked knot, Nagata.}}
{{Knot View Template|
image = carpet612.jpg |
text = A carpet.}}
{{Knot View Template|
image = Chat gpt2.gif |
text = ChatGPT bot logo.}}
|}
</div></div>
<br clear=left>

L6a3 Further Notes and Views

2024-11-21T08:38:48Z

Robert FERREOL: adding granny knot

<noinclude>Back to [[L6a3]]</noinclude><br>
{|
|- valign=top
{{Knot View Template|
image = 6a3Oberwolfach92_160.jpg |
text = Ruberman, Cochran, Melvin, Akbulut, Gompf, Kirby [http://www.maths.warwick.ac.uk/gt/Rob_Kirby_etc/6-96.html]}}
|
{{Knot View Template|
image = 6a3BySchwartz_120.png |
text = Rich Schwartz' "72" [http://www.math.umd.edu/~res/poster.html]}}
|
{{Knot View Template|
image = Triangle-Interlaced-Circle.gif |
text = Triangle interlaced with a circle, a traditional symbol of the Christian Trinity (less used in recent centuries) }}
|
{{Knot View Template|
image = Trefoil-Architectural-Equilateral-Triangle-interlaced.png |
text = An architectural trefoil (the outline of three overlapping circles) interlaced with an equilateral triangle, another old Christian Trinitarian symbol.}}

|
{{Knot View Template|
image = Noeud-de-cochon.png |
text = Closed granny knot.}}
|}

<div class="NavFrame"><div class="NavHead">Further images</div>
<div class="NavContent">
{| style="background: transparent;"
|- valign=top
{{Knot View Template|
image = Celtic flag proposed.png |
text = Celtic flag proposal.}}
{{Knot View Template|
image = Blonay-Vaud-Switzerland-flag.gif |
text = Flag of Blonay, Vaud, Switzerland.}}
{{Knot View Template|
image = Eye of Providence inside triangle interlaced with circle Venice.jpg |
text = "Eye of Providence" inside triangle interlaced with circle, Venice.}}
{{Knot View Template|
image = Six-circles-star-David.png |
text = Composed of intersecting circles.}}
|-
{{Knot View Template|
image = Hexagramm aus Nepal.jpg |
text = Hindu hexagram symbol with Aum/Om, from Nepal.}}
{{Knot View Template|
image = double boomerang.jpg |
text = Double boomerang-like Kolam and Linked knot, Nagata.}}
{{Knot View Template|
image = carpet612.jpg |
text = A carpet.}}
{{Knot View Template|
image = Chat gpt2.gif |
text = ChatGPT bot logo.}}
|}
</div></div>
<br clear=left>

File:Noeud-de-cochon.png

2024-11-21T08:33:47Z

Robert FERREOL: Knoted granny knot

== Summary ==
Knoted granny knot

L6a3 Further Notes and Views

2024-02-26T10:02:05Z

Robert FERREOL: Logo chatgpt bot

<noinclude>Back to [[L6a3]]</noinclude><br>
{|
|- valign=top
{{Knot View Template|
image = 6a3Oberwolfach92_160.jpg |
text = Ruberman, Cochran, Melvin, Akbulut, Gompf, Kirby [http://www.maths.warwick.ac.uk/gt/Rob_Kirby_etc/6-96.html]}}
|
{{Knot View Template|
image = 6a3BySchwartz_120.png |
text = Rich Schwartz' "72" [http://www.math.umd.edu/~res/poster.html]}}
|
{{Knot View Template|
image = Triangle-Interlaced-Circle.gif |
text = Triangle interlaced with a circle, a traditional symbol of the Christian Trinity (less used in recent centuries) }}
|
{{Knot View Template|
image = Trefoil-Architectural-Equilateral-Triangle-interlaced.png |
text = An architectural trefoil (the outline of three overlapping circles) interlaced with an equilateral triangle, another old Christian Trinitarian symbol.}}
|}
<div class="NavFrame"><div class="NavHead">Further images</div>
<div class="NavContent">
{| style="background: transparent;"
|- valign=top
{{Knot View Template|
image = Celtic flag proposed.png |
text = Celtic flag proposal.}}
{{Knot View Template|
image = Blonay-Vaud-Switzerland-flag.gif |
text = Flag of Blonay, Vaud, Switzerland.}}
{{Knot View Template|
image = Eye of Providence inside triangle interlaced with circle Venice.jpg |
text = "Eye of Providence" inside triangle interlaced with circle, Venice.}}
{{Knot View Template|
image = Six-circles-star-David.png |
text = Composed of intersecting circles.}}
|-
{{Knot View Template|
image = Hexagramm aus Nepal.jpg |
text = Hindu hexagram symbol with Aum/Om, from Nepal.}}
{{Knot View Template|
image = double boomerang.jpg |
text = Double boomerang-like Kolam and Linked knot, Nagata.}}
{{Knot View Template|
image = carpet612.jpg |
text = A carpet.}}
{{Knot View Template|
image = Chat gpt2.gif |
text = ChatGPT bot logo.}}
|}
</div></div>
<br clear=left>

File:Chat gpt2.gif

2024-02-26T09:58:19Z

Robert FERREOL: ChatGPT bot logo

ChatGPT bot logo

L4a1 Further Notes and Views

2023-08-15T17:13:06Z

Robert FERREOL:

<noinclude>Back to [[L4a1]].</noinclude>
<br>
{|
|- valign=top
{{Knot View Template|
image = Solomons-knot-square.png|
text = Simple squared depiction}}
|
{{Knot View Template|
image = RolfsenTable2L-4a1-C.jpg|
text = A Kolam with two cycles[http://www.scipress.org/journals/forma/frame/22.html]}}
|
{{Knot View Template|
image = 4a1HearstCastleTile_160.jpg |
text = Hearst Castle tile [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/HearstCastleTile.html]}}
|
{{Knot View Template|
image = 4a1LahavMosaic_160.jpg |
text = Mosaic seen at Kibbutz Lahav [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/LahavMosaic.html]}}
|-
{{Knot View Template|
image = San-Tome-Bergamo.jpg |
text = Carving above door of church in Italy}}
|
{{Knot View Template|
image = Solomons-knot-ornamental.png |
text = Decorative depiction}}
|
{{Knot View Template|
image = LinkingNumber2-L4a1.png |
text = (crossings along one side)}}
|
{{Knot View Template|
image = Vendee heart.png |
text = Linked hearts used as symbol of Vendée region of France}}
|- valign=top
{{Knot View Template|
image = Araldiz Manno 259.png |
text = Heraldic ornament.}}
|
{{Knot View Template|
image = Four-circles-Solomons-knot.png |
text = Composed of intersecting circles.}}
|
{{Knot View Template|
image = Solomons-ornamental-square.png |
text = Decorative fitting closely within square.}}
|
{{Knot View Template|
image = Aquileia Basilica mosaic.jpg |
text = Ancient Roman mosaic.}}
|- valign=top
{{Knot View Template|
image = Penrose rectangle Solomon's knot.png |
text = Made of two (impossible) Penrose rectangles.}}
|
{{Knot View Template|
image = Solomon's knot carpet circular.png |
text = Array of "Solomon's knots" forming overall circular patterns.}}
|
{{Knot View Template|
image = Three-L4a1-config.png |
text = Configuration of three L4a1}}
|
{{Knot View Template|
image = Solomons-knot-quadruple.png |
text = Configuration of four L4a1}}
|- valign=top
{{Knot View Template|
image = Codex Bodmer 127 (Passionary of Weissenau) 53r detail.jpg |
text = Medieval manuscript}}
|
{{Knot View Template|
image = Codex Bodmer 127 (Passionary of Weissenau) 102r detail.jpg |
text = Medieval manuscript}}
|
{{Knot View Template|
image = Codex Bodmer 127 (Passionary of Weissenau) 202v detail.jpg |
text = Medieval manuscript}}
|
{{Knot View Template|
image = Knotwork-saltire-4loops.png |
text = Rotated knotwork cross with eight L4a1 sub-configurations}}
|- valign=top
{{Knot View Template|
image = COLOR-SOLOMONS-KNOT-B.jpg |
text = Knotopologynn-diagram for "Solomon's knots"}}
|
{{Knot View Template|
image = Salomon.jpg|
text = Commercial logo}}
|}

File:Salomon.jpg

2023-08-15T17:11:24Z

Robert FERREOL: Solomon's knot

Solomon's knot

7 4 Further Notes and Views

2023-08-15T05:20:16Z

Robert FERREOL:

<noinclude>Back to [[7_4]].</noinclude>
{|
|- valign=top
{{Knot View Template|
image = Celtic-knot-linear-7crossings.png |
text = Celtic or pseudo-Celtic knot}}
{{Knot View Template|
image = mongolian74.gif |
text = Mongolian ornament}}
{{Knot View Template|
image = SusanWilliamsMedallion_160.jpg |
text = Susan Williams' medallion [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/SusanWilliamsMedallion.html], the "Endless knot" of Buddhism [http://en.wikipedia.org/wiki/Endless_knot]}}

{{Knot View Template|
image = Endless knot outlined.png |
text = Ornamental "Endless knot"}}
|- valign=top
{{Knot View Template|
image = KornikKnot_160.jpg |
text = a knot seen at the Castle of Kornik [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/KornikKnot.html]}}
{{Knot View Template|
image = Takara-4harts-C7.jpg |
text = A 7-4 knot reduced from TakaraMusubi with 9 crossings
[http://intervision.aadau.net/]}}

{{Knot View Template|
image = TakaraMusubi-C9.jpg |
text = TakaraMusubi knot seen in Japanese symbols, or Kolam in South India
[http://intervision.aadau.net/]}}

{{Knot View Template|
image = Ashtamangala-Endless-knot.jpg |
text = Buddhist Endless Knot}}
|- valign=top
{{Knot View Template|
image = Endless-knot-Shrivatsa.jpg |
text = Ornamental Endless Knot}}

{{Knot View Template|
image = Duerer-knot.jpg |
text = Albrecht Dürer knot, 16th-century}}
{{Knot View Template|
image = LaserCut_7_4_120.jpg |
text = A laser cut by Tom Longtin [http://mysite.verizon.net/t.longtin/knot_atlas/index.html]}}

{{Knot View Template|
image = Interwoven unicursal hexagram.gif |
text = Unicursal hexagram of occultism}}
|- valign=top
{{Knot View Template|
image = symboleraelien.jpg |
text = Logo of the raelian sect}}
{{Knot View Template|
image = p11.gif |
text = Lissajous curve : x=cos 3t , y=sin 2t, z=sin 7t}}
{{Knot View Template|
image = Europa2023.gif|
text = French europa stamp 2023}}

|}

7 4 Further Notes and Views

2023-08-15T05:16:41Z

Robert FERREOL: adding new picture

File:Europa2023.gif

2023-08-15T05:13:32Z

Robert FERREOL: europa stamp 2023

europa stamp 2023

L8a14 Further Notes and Views

2022-06-30T09:11:37Z

Robert FERREOL: good name

<noinclude>Back to [[L8a14]].</noinclude>
{|
|- valign=top
{{Knot View Template|
image = StockExchangePalace_160.jpg |
text = Floor of the Stock Exchange [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/StockExchangePalace.html]}}
|
{{Knot View Template|
image = Star-lakshmi.gif |
text = Represented as two interlaced squares}}
|
{{Knot View Template|
image = IstanbulFloorMosaic.jpg |
text = A mosaic seen on an Istanbul floor}}
|
{{Knot View Template|
image = Jaromer-Czech-CoA.png |
text = Coat of arms of Jaroměř, Czech Republic}}
|- valign=top
{{Knot View Template|
image = St-Savior-Jersey-UK-COA.gif |
text = Coat of arms of St. Savior, Jersey, Channel Islands, depicting Crown of Thorns religious symbol}}
|
{{Knot View Template|
image = Sameba Cathedral Tbilisi 13.jpg |
text = Cathedral in Tbilisi, Georgia}}
|
{{Knot View Template|
image = Mozota-Coatofarms.gif |
text = Coat of arms of Mozota, Spain}}
|
{{Knot View Template|
image = Decorative motif of interlaced squares, San Pancrazio, Florence.jpg |
text = Decorative motif of interlaced squares, San Pancrazio, Florence}}
|- valign=top
{{Knot View Template|
image = Macedonian cross.png |
text = Macedonian cross}}
|
{{Knot View Template|
image = 8crossings-link-3D.PNG |
text = 3D depiction}}
|
{{Knot View Template|
image = Visitacao Braga Brazao.jpg |
text = ''Arma Christi'' carving in monastery in Portugal}}
|
{{Knot View Template|
image = Handewitt Schleswig-Holstein arms oak.png |
text = Handewitt, Schleswig-Holstein oak leaves and acorns}}
|
|- valign=top
{{Knot View Template|
image = Onam festival flower carpet Maspraveen.jpg |
text = Flower carpet, south India}}
|
{{Knot View Template|
image = Flower carpet onam . irvin 01.jpg |
text = Flower carpet, south India}}
|
{{Knot View Template|
image = Persian or central Asian tile detail 15th century.JPG |
text = Islamic art tile}}

|
{{Knot View Template|
image = 8crossingsmarocco.jpg |
text = Moroccan craft}}
|- valign=top
{{Knot View Template|
image = Murato.jpg |
text = Link on a church of Murato,Corsica }}

|
{{Knot View Template|
image = senda malaga.png |
text = Logo of a spanish hiking trail}}

|}

L8a14 Further Notes and Views

2022-06-30T09:06:45Z

Robert FERREOL: adding new picture

<noinclude>Back to [[L8a14]].</noinclude>
{|
|- valign=top
{{Knot View Template|
image = StockExchangePalace_160.jpg |
text = Floor of the Stock Exchange [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/StockExchangePalace.html]}}
|
{{Knot View Template|
image = Star-lakshmi.gif |
text = Represented as two interlaced squares}}
|
{{Knot View Template|
image = IstanbulFloorMosaic.jpg |
text = A mosaic seen on an Istanbul floor}}
|
{{Knot View Template|
image = Jaromer-Czech-CoA.png |
text = Coat of arms of Jaroměř, Czech Republic}}
|- valign=top
{{Knot View Template|
image = St-Savior-Jersey-UK-COA.gif |
text = Coat of arms of St. Savior, Jersey, Channel Islands, depicting Crown of Thorns religious symbol}}
|
{{Knot View Template|
image = Sameba Cathedral Tbilisi 13.jpg |
text = Cathedral in Tbilisi, Georgia}}
|
{{Knot View Template|
image = Mozota-Coatofarms.gif |
text = Coat of arms of Mozota, Spain}}
|
{{Knot View Template|
image = Decorative motif of interlaced squares, San Pancrazio, Florence.jpg |
text = Decorative motif of interlaced squares, San Pancrazio, Florence}}
|- valign=top
{{Knot View Template|
image = Macedonian cross.png |
text = Macedonian cross}}
|
{{Knot View Template|
image = 8crossings-link-3D.PNG |
text = 3D depiction}}
|
{{Knot View Template|
image = Visitacao Braga Brazao.jpg |
text = ''Arma Christi'' carving in monastery in Portugal}}
|
{{Knot View Template|
image = Handewitt Schleswig-Holstein arms oak.png |
text = Handewitt, Schleswig-Holstein oak leaves and acorns}}
|
|- valign=top
{{Knot View Template|
image = Onam festival flower carpet Maspraveen.jpg |
text = Flower carpet, south India}}
|
{{Knot View Template|
image = Flower carpet onam . irvin 01.jpg |
text = Flower carpet, south India}}
|
{{Knot View Template|
image = Persian or central Asian tile detail 15th century.JPG |
text = Islamic art tile}}

|
{{Knot View Template|
image = 8crossingsmarocco.jpg |
text = Moroccan craft}}
|- valign=top
{{Knot View Template|
image = Murato.jpg |
text = Link on a church of Murato,Corsica }}

|
{{Knot View Template|
image = logo malaga.jpg |
text = logo of a spanish hiking trail}}

|}

File:Senda malaga.png

2022-06-30T09:02:57Z

Robert FERREOL: logo of a spanish hiking trail

logo of a spanish hiking trail

K12a1019 Notes and Views

2020-12-30T09:03:43Z

Robert FERREOL: new image on a spheroid

<noinclude>Back to [[K12a1019]].</noinclude>

{|
|- valign=top
{{Knot View Template|
image = K12a1019.png |
text = Knotscape}}
|
{{Knot View Template|
image =12crossings-rose-rhodonea-limacon-symmetrical-knot.png |
text = Three-fold symmetrical representation}}
|
{{Knot View Template|
image = 12crossings.jpg |
text = K12a1019 as a geodesic line of the oblate spheroid}}
|}

File:12crossings.jpg

2020-12-30T08:55:47Z

Robert FERREOL: K12a1019 as a geodesic line of the oblate spheroid

K12a1019 as a geodesic line of the oblate spheroid

9 40 Further Notes and Views

2020-12-29T20:03:44Z

Robert FERREOL: new picture

<noinclude>Back to [[9_40]].</noinclude>
{|
|- valign=top

{{Knot View Template|
image = 9crossings-knot-symmetrical.png|
text = In three-fold symmetrical form}}
|
{{Knot View Template|
image = 9crossings-knot-symmetric-triangles-pseudo-valknut.png|
text = Symmetrical triangular form}}
|
{{Knot View Template|
image = 9crossings-knot-symmetric-triangles-quasi-valknut.png|
text = (less open)}}
|

{{Knot View Template|
image = 9crossings-knot-symmetric-triangles-quasi-valknut-alternate.png|
text = (alternate)}}

|
{{Knot View Template|
image = noeud triangle.png|
text = Variant}}
|- valign=top

{{Knot View Template|
image = 9.40epitrochoid.jpg|
text = Obtained by an epitrochoid.}}

|
{{Knot View Template|
image = cylindric9.40.png|
text = Cylindrical depiction.}}
|
{{Knot View Template|
image =9.40ellipsoid.png|
text = 9.40 as a geodesic line of the oblate spheroid}}
|

{{Knot View Template|
image = Chaise_alsacienne.jpg|
text = Photo of an alsatian chair, musée de l'oeuvre Notre Dame, Strasbourg, France.}}

|}

File:9.40ellipsoid.png

2020-12-29T20:01:12Z

Robert FERREOL: 9.40 as a geodesic line of the oblate spheroid

9.40 as a geodesic line of the oblate spheroid

9 40 Further Notes and Views

2020-12-29T14:40:32Z

Robert FERREOL: new picture

<noinclude>Back to [[9_40]].</noinclude>
{|
|- valign=top

{{Knot View Template|
image = 9crossings-knot-symmetrical.png|
text = In three-fold symmetrical form}}
|
{{Knot View Template|
image = 9crossings-knot-symmetric-triangles-pseudo-valknut.png|
text = Symmetrical triangular form}}
|
{{Knot View Template|
image = 9crossings-knot-symmetric-triangles-quasi-valknut.png|
text = (less open)}}
|
{{Knot View Template|
image = 9crossings-knot-symmetric-triangles-quasi-valknut-alternate.png|
text = (alternate)}}

|
{{Knot View Template|
image = noeud triangle.png|
text = Variant}}
|- valign=top

{{Knot View Template|
image = 9.40epitrochoid.jpg|
text = Obtained by an epitrochoid.}}

|
{{Knot View Template|
image = cylindric9.40.png|
text = Cylindrical depiction.}}

|
{{Knot View Template|
image = Chaise_alsacienne.jpg|
text = Photo of an alsatian chair, musée de l'oeuvre Notre Dame, Strasbourg, France.}}

|}

File:9.40epitrochoid.jpg

2020-12-29T14:37:39Z

Robert FERREOL: knot 9.40 obtained by an epitrochoid

knot 9.40 obtained by an epitrochoid

8 18 Further Notes and Views

2020-12-29T13:54:33Z

Robert FERREOL: new picture

<noinclude>Back to [[8_18]].</noinclude>
<br>
{|
|- valign=top
{{Knot View Template|
image = IGKT_h120.jpg |
text = Logo of the International Guild of Knot Tyers [http://www.igkt.net/]}}
|
{{Knot View Template|
image = ABeneficenciaFamiliar_120.jpg |
text = A charity logo in Porto [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/ABeneficenciaFamiliar.html]}}
|
{{Knot View Template|
image = LaserCut_8_18_120.jpg |
text = A laser cut by Tom Longtin [http://mysite.verizon.net/t.longtin/knot_atlas/index.html]}}
|
{{Knot View Template|
image = Bar-knot-simplest-decorative.gif |
text = Knot in (pseudo-)Celtic decorative form}}
|- valign=top
{{Knot View Template|
image = 8crossings-4circles.png |
text = Less symmetrical}}
|
{{Knot View Template|
image = 8crossing-circular.png |
text = Within outer circle}}

|
{{Knot View Template|
image = noeudcarre.png |
text = Impossible figure}}
|
{{Knot View Template|
image = mongolian8.18.gif |
text = Mongolian ornament}}

|- valign=top
{{Knot View Template|
image = Carrick mat by Brianetta.jpg |
text = Jump rope knot}}
|
{{Knot View Template|
image = Belt-design.jpg |
text = Belt design}}
|
{{Knot View Template|
image = Bondage_knot.jpg |
text = Bondage knot}}
|
{{Knot View Template|
image = fhdebifd.png |
text = Spheric depiction}}

|- valign=top
{{Knot View Template|
image = Képi Infanterie Sous-Lieutenant Armée Française.jpg|
text= A "Hungarian Knot", decorating French Military uniforms.
}}
|
{{Knot View Template|
image = carpetswatter8.18.jpg|
text= Carpet swatter.
}}

|
{{Knot View Template|
image = Hlfghihckajjkbhp.png|
text= Geodesic of the prolate ellipsoid.
}}

|
{{Knot View Template|
image = 8.18epitrochoid.jpg|
text= Obtained with an epitrochoid.
}}

|}

File:8.18epitrochoid.jpg

2020-12-29T13:45:36Z

Robert FERREOL: 8.18 knot by epitrochoid

8.18 knot by epitrochoid

8 18 Further Notes and Views

2020-12-28T15:42:48Z

Robert FERREOL: adding picture

File:Hlfghihckajjkbhp.png

2020-12-28T15:40:30Z

Robert FERREOL: Geodesic of the prolate ellipsoid

Geodesic of the prolate ellipsoid

8 18 Further Notes and Views

2020-10-06T12:07:07Z

Robert FERREOL: adding picture

File:Carpetswatter8.18.jpg

2020-10-06T12:03:15Z

Robert FERREOL: carpet swatter

carpet swatter

5 1 Further Notes and Views

2020-04-28T15:31:47Z

Robert FERREOL:

<noinclude>Back to [[5_1]].</noinclude>
<br>
{|
|- valign=top
{{Knot View Template|
image = SolomonsSealKnot5a-C.jpg|
text = A kolam of a 2x3 dot array}}
{{Knot View Template|
image = 5_1Interlink_160.gif |
text = The VISA Interlink Logo [http://www.cardweb.com/cardtrak/news/2001/september/18a.html]}}
{{Knot View Template|
image = United States Bicentennial star 1976 (geometry).png |
text = Version of the [http://en.wikipedia.org/wiki/United_States_Bicentennial US bicentennial] emblem}}
|- valign=top
{{Knot View Template|
image = PentagonalTable_120.jpg |
text = A pentagonal table by Bob Mackay [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/PentagonalTable.html]}}
{{Knot View Template|
image = UtahSPlogo.jpg |
text = The Utah State Parks logo}}
{{Knot View Template|
image = Penrose pentagram.png |
text = As impossible object ("Penrose" pentagram)}}
|- valign=top
{{Knot View Template|
image = Pentagram-ribbon-folded.png |
text = Folded ribbon which is single-sided (more complex version of Möbius Strip).}}
{{Knot View Template|
image = 5crossing-trefplus2.png |
text = Non-pentagonal shape.}}
{{Knot View Template|
image = Pentagram-of-circles.png |
text = Pentagram of circles.}}
|- valign=top
{{Knot View Template|
image = Five-circles-pentagram.png |
text = Alternate pentagram of intersecting circles.}}
{{Knot View Template|
image = Pentgx3D.jpg |
text = 3D-looking rendition.}}
{{Knot View Template|
image = ShirtInLisboa_160.jpg |
text = Partial view of US bicentennial logo on a shirt seen in Lisboa [http://www.math.toronto.edu/~drorbn/Talks/Oporto-0407/KnotsInLisboa.html]}}
|- valign=top
{{Knot View Template|
image = 10crossings-twosymmetric-nonprime.png |
text = Non-prime knot with two 5_1 configurations on a closed loop.}}
{{Knot View Template|
image = lhkejgdpgkodiill.png |
text = Knotted epitrochoid}}
{{Knot View Template|
image = 5 1Wien.jpg |
text = Sum of two 5_1s, Vienna, orthodox church}}

|}


<font size=-2 color=orange>This sentence was last edited by Dror.</font>
<font size=-2 color=green>Sometime later, Scott added this sentence.</font>

File:5 1Wien.jpg

2020-04-28T15:28:28Z

Robert FERREOL: Greek church in Wien

Greek church in Wien

Ornamental depictions of links with 12 crossings

2020-04-28T15:06:50Z

Robert FERREOL:

Some decorative depictions of links with 12 crossings :

;I) With two component

;a) Components are loops
<gallery>
Image:Two-interlaced-hexagrams.png|Two interlaced open hexagrams
Image:Ccross-two-link.png|Quasi-Celtic two-loop link
Image:12crossing-twosymmetric-link.png|Two loops
Image:Link12-round.png|Two loops
Image:Three-L4a1.png|Two-loop link
Image:Four-loop-interlaced-circle.png|Four-fold looping interlaced with circle (two-loop link)
Image:Noeudmongol.jpg|Mongolian ornament, equivalent to preceding
Image:Pleter50.png|Equivalent to preceding
Image:12-crossing-link Tallara Lousame Galicia Spain.jpg|Sculpture of preceding
Image:Carreau.jpg|Tiling ; equivalent to preceding
Image:assiette.sicile.jpg|Sicilian plate, also equivalent
Image:12crossings-pseudo-Celtic-link.png|One crossing of [[K13a1345]] eliminated, converting from knot to link...
</gallery>

;b) One component is knoted
<gallery>
Image:Triquetra-double-interlaced.png|Two mutually-interlaced triquetras
Image:Trefoil-in-trefoil.png|Trefoil interlinked with smaller trefoil
Image:Two-trefoils-triangles-link.png|Two interlinked trefoils
Image:12crossing-link-inrectangle.png|Two interlinked trefoils inside rectangle
Image:Two-trefoils-granny-12crossings.png|Sum of two trefoils linked with a loop
</gallery>

;II) With three components
<gallery>
Image:Celtic-knot-square-3loops.png|3-loop link in the form of a quasi-Celtic knot
Image:Triplesalomon.jpeg|Same link in this work of the Mexican artist Daniela Azuela
Image:Cross of Uppland Runestone-.jpg|Ca. 1000 A.D. runestone, equivalent to preceding
Image:12-crossings-squares-16.png|Equivalent link in square form
Image:Kirche_Wien.jpg|in the Greek Orthodox Church in Wien
Image:Three-loop-link-12-crossings-alternate.png|(alternate version)
Image:Brunnian-3-not-Borromean.gif|Three-component [[Brunnian link]]
Image:Brunnian-link-12crossings-nonBorromean-quasi-Arabesque.png|More ornate Brunnian link depiction
Image:Three-L4a1-config.png|Three-loop link with three [[L4a1]] configurations
Image:12crossings-pseudo-Borromean.png|Three-loop link
Image:Triang-two-circ.png|Triangle and two circles
Image:12crossings-threesymmetric-link.png|Three loops symmetric
Image:12crossings-decorative-threefold-incircle-link.png|Three loops symmetric
Image:Two-trefoils-loop-12crossings.png|Two trefoils and one loop
</gallery>

;III) With four loops
<gallery>
Image:4squares-12crossings.png|Four linked squares (alternated)
Image:4intersecting-rounded-rectangles.png|Variant
Image:fourcircles.jpg|Variant with circles
Image:noeudsCarres-2.png|Variant with rectangles as an impossible object
Image:adiadgib.jpg|Variant on the sphere ; the crossings are the vertices of the cuboctahedron
Image:Borromean-plus-triangle.png|Four loops (Borromean + triangle)
Image:stemariemajeure.jpg|Basilica of Saint Mary Major (not alternated)
</gallery>

;IV) With six loops
<gallery>
Image:Six-rings.png|Six rings
Image:Six-link-closed-chain-Hisham-Umayyad-palace-Jericho.jpg|Decoration equivalent to a circle of six interlinked loops
</gallery>

For ornamental depictions of knots with 12 crossings, see [[K12a477]], [[K12a503]], [[K12a541]], [[K12a561]], [[K12a975]], [[K12a991]], [[K12a1019]], [[K12a1210]], [[K12n242]], and (non-prime) [[:Image:Trefoil-of-trefoils.png]], [[:Image:Celtic-knot-insquare-green-transparentbg.png]], [[:Image:Three-figure8-knot triang1.png]], and [[:Image:Three-figure8-knot triang2.png]].

File:Kirche Wien.jpg

2020-04-28T15:02:50Z

Robert FERREOL: In the greek church in Vienna

In the greek church in Vienna

Ornamental depictions of links with 12 crossings

2019-02-06T13:24:40Z

Robert FERREOL: new picture

Some decorative depictions of links with 12 crossings :

;I) With two component

;a) Components are loops
<gallery>
Image:Two-interlaced-hexagrams.png|Two interlaced open hexagrams
Image:Ccross-two-link.png|Quasi-Celtic two-loop link
Image:12crossing-twosymmetric-link.png|Two loops
Image:Link12-round.png|Two loops
Image:Three-L4a1.png|Two-loop link
Image:Four-loop-interlaced-circle.png|Four-fold looping interlaced with circle (two-loop link)
Image:Noeudmongol.jpg|Mongolian ornament, equivalent to preceding
Image:Pleter50.png|Equivalent to preceding
Image:12-crossing-link Tallara Lousame Galicia Spain.jpg|Sculpture of preceding
Image:Carreau.jpg|Tiling ; equivalent to preceding
Image:assiette.sicile.jpg|Sicilian plate, also equivalent
Image:12crossings-pseudo-Celtic-link.png|One crossing of [[K13a1345]] eliminated, converting from knot to link...
</gallery>

;b) One component is knoted
<gallery>
Image:Triquetra-double-interlaced.png|Two mutually-interlaced triquetras
Image:Trefoil-in-trefoil.png|Trefoil interlinked with smaller trefoil
Image:Two-trefoils-triangles-link.png|Two interlinked trefoils
Image:12crossing-link-inrectangle.png|Two interlinked trefoils inside rectangle
Image:Two-trefoils-granny-12crossings.png|Sum of two trefoils linked with a loop
</gallery>

;II) With three components
<gallery>
Image:Celtic-knot-square-3loops.png|3-loop link in the form of a quasi-Celtic knot
Image:Triplesalomon.jpeg|Same link in this work of the Mexican artist Daniela Azuela
Image:Cross of Uppland Runestone-.jpg|Ca. 1000 A.D. runestone, equivalent to preceding
Image:12-crossings-squares-16.png|Equivalent link in square form
Image:Three-loop-link-12-crossings-alternate.png|(alternate version)
Image:Brunnian-3-not-Borromean.gif|Three-component [[Brunnian link]]
Image:Brunnian-link-12crossings-nonBorromean-quasi-Arabesque.png|More ornate Brunnian link depiction
Image:Three-L4a1-config.png|Three-loop link with three [[L4a1]] configurations
Image:12crossings-pseudo-Borromean.png|Three-loop link
Image:Triang-two-circ.png|Triangle and two circles
Image:12crossings-threesymmetric-link.png|Three loops symmetric
Image:12crossings-decorative-threefold-incircle-link.png|Three loops symmetric
Image:Two-trefoils-loop-12crossings.png|Two trefoils and one loop
</gallery>

;III) With four loops
<gallery>
Image:4squares-12crossings.png|Four linked squares (alternated)
Image:4intersecting-rounded-rectangles.png|Variant
Image:fourcircles.jpg|Variant with circles
Image:noeudsCarres-2.png|Variant with rectangles as an impossible object
Image:adiadgib.jpg|Variant on the sphere ; the crossings are the vertices of the cuboctahedron
Image:Borromean-plus-triangle.png|Four loops (Borromean + triangle)
Image:stemariemajeure.jpg|Basilica of Saint Mary Major (not alternated)
</gallery>

;IV) With six loops
<gallery>
Image:Six-rings.png|Six rings
Image:Six-link-closed-chain-Hisham-Umayyad-palace-Jericho.jpg|Decoration equivalent to a circle of six interlinked loops
</gallery>

For ornamental depictions of knots with 12 crossings, see [[K12a477]], [[K12a503]], [[K12a541]], [[K12a561]], [[K12a975]], [[K12a991]], [[K12a1019]], [[K12a1210]], [[K12n242]], and (non-prime) [[:Image:Trefoil-of-trefoils.png]], [[:Image:Celtic-knot-insquare-green-transparentbg.png]], [[:Image:Three-figure8-knot triang1.png]], and [[:Image:Three-figure8-knot triang2.png]].

File:Triplesalomon.jpeg

2019-02-03T17:45:41Z

Robert FERREOL: Knot with 12 crossings and 3 loops

Knot with 12 crossings and 3 loops

9 23 Further Notes and Views

2019-01-24T09:56:44Z

Robert FERREOL: Other picture

<noinclude>Back to [[9 23]].</noinclude>
<br>
{|
|- valign=top
{{Knot View Template|
image = 9crossings-2symmetrical.png |
text = Symmetrical decorative knot}}
|{{Knot View Template|
image = 9crossing-knot symmetrical grid.png |
text = With crossings on 3x3 grid}}
|{{Knot View Template|
image = Cjdfjjhd.png |
text = Depiction with two axes of symmetry}}
|{{Knot View Template|
image = mongolian632.2.gif |
text = Mongolian ornament (two crossings are unnecessary)}}
|- valign=top
{{Knot View Template|
image = mongolian9.23.gif |
text = Mongolian ornament, sum of two 9.23}}
|{{Knot View Template|
image = logo-icmc.jpg |
text = Logo of the [http://www.icmc.usp.br/ ICMC-USP], Brazil}}

|{{Knot View Template|
image = Jpmdgfieodphjphg.png |
text = Other depicture with central symmetry by Alain Esculier}}
|}

File:Jpmdgfieodphjphg.png

2019-01-24T09:55:37Z

Robert FERREOL:

8 19 Further Notes and Views

2019-01-24T09:51:56Z

Robert FERREOL: Yes, 8_19, not 8_18...

[[8_19]] is the first non-homologically thin knot in the Rolfsen table. (That is, it's the first knot whose Khovanov homology has 'off-diagonal' elements.)

{|
|- valign=top
{{Knot View Template|
image = 8-19-knotscape.png|
text = Knotscape}}
|
{{Knot View Template|
image = 8crossing-symmetrical-nonalternating.png|
text = Symmetrical form ; (3,4) torus knot}}
|
{{Knot View Template|
image = Trueloversknot.jpg|
text = True-lover's knot with sticked free ends }}
{{Knot View Template|
image = Pkamiejfilefkplj.png|
text = Equal to the previous, from knotilus }}
{{Knot View Template|
image = 1,-2,3,4,-5,-1,2,-3,6,-7,8,5,-4,-6,7,-8.png|
text = Pretzel knot P(2,-3,-3) }}
{{Knot View Template|
image = logo-forumdelentrepreneuriat.png|
text = French logo }}
{{Knot View Template|
image = IMG 20180618 140044.jpg|
text = Seen in Singapore }}

|}

9 40 Further Notes and Views

2019-01-24T08:48:03Z

Robert FERREOL:

<noinclude>Back to [[9_40]].</noinclude>
{|
|- valign=top

{{Knot View Template|
image = 9crossings-knot-symmetrical.png|
text = In three-fold symmetrical form}}
|
{{Knot View Template|
image = 9crossings-knot-symmetric-triangles-pseudo-valknut.png|
text = Symmetrical triangular form}}
|
{{Knot View Template|
image = 9crossings-knot-symmetric-triangles-quasi-valknut.png|
text = (less open)}}
|
{{Knot View Template|
image = 9crossings-knot-symmetric-triangles-quasi-valknut-alternate.png|
text = (alternate)}}

|- valign=top
{{Knot View Template|
image = noeud triangle.png|
text = Variant}}
|
{{Knot View Template|
image = Chaise_alsacienne.jpg|
text = Photo of an alsatian chair, musée de l'oeuvre Notre Dame, Strasbourg, France.}}
|
{{Knot View Template|
image = cylindric9.40.png|
text = Cylindrical depiction.}}
|}

8 18 Further Notes and Views

2018-06-19T16:19:31Z

Robert FERREOL:

<noinclude>Back to [[8_18]].</noinclude>
<br>
{|
|- valign=top
{{Knot View Template|
image = IGKT_h120.jpg |
text = Logo of the International Guild of Knot Tyers [http://www.igkt.net/]}}
|
{{Knot View Template|
image = ABeneficenciaFamiliar_120.jpg |
text = A charity logo in Porto [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/ABeneficenciaFamiliar.html]}}
|
{{Knot View Template|
image = LaserCut_8_18_120.jpg |
text = A laser cut by Tom Longtin [http://mysite.verizon.net/t.longtin/knot_atlas/index.html]}}
|
{{Knot View Template|
image = Bar-knot-simplest-decorative.gif |
text = Knot in (pseudo-)Celtic decorative form}}
|- valign=top
{{Knot View Template|
image = 8crossings-4circles.png |
text = Less symmetrical}}
|
{{Knot View Template|
image = 8crossing-circular.png |
text = Within outer circle}}

|
{{Knot View Template|
image = noeudcarre.png |
text = Impossible figure}}
|
{{Knot View Template|
image = mongolian8.18.gif |
text = Mongolian ornament}}

|- valign=top
{{Knot View Template|
image = Carrick mat by Brianetta.jpg |
text = Jump rope knot}}
|
{{Knot View Template|
image = Belt-design.jpg |
text = Belt design}}
|
{{Knot View Template|
image = Bondage_knot.jpg |
text = Bondage knot}}
|
{{Knot View Template|
image = fhdebifd.png |
text = Spheric depiction}}

|- valign=top

{{Knot View Template|
image = Képi Infanterie Sous-Lieutenant Armée Française.jpg|
text= A "Hungarian Knot", decorating French Military uniforms.}}
|

{{Knot View Template|
image = IMG 20180618 140044.jpg|
text= Logo of the tanjong pagar community club, Singapore.

}}
|}

8 18 Further Notes and Views

2018-06-19T16:15:48Z

Robert FERREOL: adding a new picture

<noinclude>Back to [[8_18]].</noinclude>
<br>
{|
|- valign=top
{{Knot View Template|
image = IGKT_h120.jpg |
text = Logo of the International Guild of Knot Tyers [http://www.igkt.net/]}}
|
{{Knot View Template|
image = ABeneficenciaFamiliar_120.jpg |
text = A charity logo in Porto [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/ABeneficenciaFamiliar.html]}}
|
{{Knot View Template|
image = LaserCut_8_18_120.jpg |
text = A laser cut by Tom Longtin [http://mysite.verizon.net/t.longtin/knot_atlas/index.html]}}
|
{{Knot View Template|
image = Bar-knot-simplest-decorative.gif |
text = Knot in (pseudo-)Celtic decorative form}}
|- valign=top
{{Knot View Template|
image = 8crossings-4circles.png |
text = Less symmetrical}}
|
{{Knot View Template|
image = 8crossing-circular.png |
text = Within outer circle}}

|
{{Knot View Template|
image = noeudcarre.png |
text = Impossible figure}}
|
{{Knot View Template|
image = mongolian8.18.gif |
text = Mongolian ornament}}

|- valign=top
{{Knot View Template|
image = Carrick mat by Brianetta.jpg |
text = Jump rope knot}}
|
{{Knot View Template|
image = Belt-design.jpg |
text = Belt design}}
|
{{Knot View Template|
image = Bondage_knot.jpg |
text = Bondage knot}}
|
{{Knot View Template|
image = fhdebifd.png |
text = Spheric depiction}}

|- valign=top
{{Knot View Template|
image = Képi Infanterie Sous-Lieutenant Armée Française.jpg|
text= A "Hungarian Knot", decorating French Military uniforms.

{{Knot View Template|
image = IMG 20180618 140044.jpg|
text= logo of the tanjong pagar community club, Singapore.

}}
|}

File:IMG 20180618 140044.jpg

2018-06-19T16:12:39Z

Robert FERREOL: logo of the tanjong pagar community club, singapore

logo of the tanjong pagar community club, singapore

File:Vitrail.jpg

2018-06-04T18:47:14Z

Robert FERREOL: Stained glass church in Paris

Stained glass church in Paris

3 1 Further Notes and Views

2018-06-04T09:59:59Z

Robert FERREOL: /* Non-prime (compound) versions */ new picture

The [[3_1|trefoil]] is perhaps the easiest knot to find in "nature", and is topologically equivalent to the interlaced form of the common Christian and pagan "triquetra" symbol [http://en.wikipedia.org/wiki/Triquetra]:

{| style="background: transparent;"
|- valign=top
{{Knot View Template|
image = CaixaGeral_160.jpg |
text = Logo of Caixa Geral de Depositos, Lisboa [http://www.math.toronto.edu/~drorbn/Talks/Oporto-0407/KnotsInLisboa.html]|
}}
{{Knot View Template|
image = hart-knot-C.jpg|
text = A knot consists of two harts in Kolam
[http://intervision.aadau.net/]|
}}
{{Knot View Template|
image = Triquetra-Vesica-solid.png |
text = A basic form of the interlaced Triquetra; as a Christian symbol, it refers to the Trinity|
}}
{{Knot View Template|
image = Blue Trefoil Knot.png |
text = 3D depiction |
}}
|}

<div class="NavFrame"><div class="NavHead">Further images...</div>
<div class="NavContent">
{| style="background: transparent;"
|- valign=top
{{Knot View Template|
image = Trefoil-triquetra-circular-arcs-around-triangle.png |
text = Trefoil/triquetra without outside corners (made from straight lines and 240° circular arcs)|
}}
{{Knot View Template|
image = Triquetra-Vesica.png |
text = Triquetra made from circular arc ribbons|
}}
{{Knot View Template|
image = Triquetra-tightly-knotted.png |
text = Tightly-knotted form|
}}
{{Knot View Template|
image = Vodicka triquetra.png |
text = Celtic-style|
}}
|- valign=top
{{Knot View Template|
image = KnottedBox_160.jpg |
text = A Knotted Box [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/KnottedBox.html]|
}}
{{Knot View Template|
image = HollanderYork_160.jpg |
text = A trefoil near the Hollander York Gallery [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/HollanderYork.html]|
}}
{{Knot View Template|
image = Three-circles-Trefoil.png |
text = Trefoil of three intersecting circles|
}}
{{Knot View Template|
image = Trefoil-non-3-symm.png |
text = Trefoil depicted in non-threefold form
}}
|- valign=top
{{Knot View Template|
image = One-Twist Trefoil.png |
text = 3D depiction in non-threefold form
}}
{{Knot View Template|
image = hagfish-knotting.gif |
text = A hagfish tying itself in a knot to escape capture. [http://oceanlink.island.net/oinfo/hagfish/hagfish.html]|
}}
{{Knot View Template|
image = Valknut-Symbol-triquetra.png |
text = One version of the Germanic "Valknut" symbol|
}}
{{Knot View Template|
image = KenyanStone_160.jpg |
text = A Kenyan Stone [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/KenyanStone.html]|
}}
|- valign=top
{{Knot View Template|
image = Trefoil-square.png |
text = Square depiction|
}}
{{Knot View Template|
image = Trefoil-Triquetra.png |
text = In the form of an architectural trefoil|
}}
{{Knot View Template|
image = Trefoil-triquetra-rhodonea-rose-limacon.png |
text = Polar equation curve.|
}}
{{Knot View Template|
image = Valknut-Symbol-triquetra-alternate.png |
text = Alternate Valknut depiction
}}
|- valign=top
{{Knot View Template|
image = Overhand-loop.png |
text = Simple overhand knot of practical knot-tying|
}}
{{Knot View Template|
image = Overhand-folded-ribbon-pentagram.png |
text = Tightly folded pentagonal overhand knot|
}}
{{Knot View Template|
image = Trefoil-square-centerline.png |
text = Visually fancier square trefoil|
}}
{{Knot View Template|
image = Impossible trefoil knot Isometric.png |
text = Trefoil knot as impossible object|
}}
|- valign=top
{{Knot View Template|
image = TriquetraCaixaGeral.png |
text = Logo of the Caixa Geral de Depósitos with white background|
}}
{{Knot View Template|
image = Auryn_120.gif |
text = The NeverEnding Story logo is a connected sum of two trefoils. [http://www.thealmightyguru.com/Reviews/NeverendingStory/NeverendingStory.html]|
}}
{{Knot View Template|
image = RopeTrick_160.jpg |
text = Mike Hutchings' Rope Trick [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/RopeTrick/index.html]|
}}
{{Knot View Template|
image = DylansTrefoil_120.jpg |
text = Thurston's Trefoil - Figure Eight Trick [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/TrefoilFigureEight/index.html]|
}}
|- valign=top
{{Knot View Template|
image = KnottedPencil_160.jpg |
text = A Knotted Pencil [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/KnottedPencil.html]|
}}
{{Knot View Template|
image = BancoDoBrasil_160.jpg |
text = Banco Do Brasil [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/BancoDoBrasil.html]|
}}
|}

===Non-prime (compound) versions===
<gallery>
Image:Granny-knot-6-crossings.png|Two trefoils (single-closed-loop version of the "granny knot" of practical knot-tying).
Image:Square-knot-6-crossings.png|Two trefoils (single-closed-loop version of the "square knot" of practical knot-tying)
Image:Blue Square Knot.png|3D square knot
Image:3trefoil-9crossings.gif|Three trefoils (symmetrical).
Image:Celtic-knot-insquare-green-transparentbg.png|Four trefoils (Celtic or pseudo-Celtic decorative knot which fits in square)
Image:Trefoil-of-trefoils.png|Three trefoils along a closed loop which itself is knotted as a trefoil.
Image : multan.jpg|Sum of four trefoils, Multan, Pakistan
</gallery>
For configurations of two trefoils along a closed loop which are prime, see [[8_15]] and [[10_120]]. For a configuration of three trefoils along a closed loop which is prime, see [[K13a248]]. For a prime link consisting of two joined trefoils, see [[L10a108]].
</div></div>
<br clear=left>

File:Multan.jpg

2018-06-04T09:58:25Z

Robert FERREOL: Sum of four trefoils, Multan, Pakistan

Sum of four trefoils, Multan, Pakistan

L8a14 Further Notes and Views

2018-06-04T09:49:38Z

Robert FERREOL: new picture

<noinclude>Back to [[L8a14]].</noinclude>
{|
|- valign=top
{{Knot View Template|
image = StockExchangePalace_160.jpg |
text = Floor of the Stock Exchange [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/StockExchangePalace.html]}}
|
{{Knot View Template|
image = Star-lakshmi.gif |
text = Represented as two interlaced squares}}
|
{{Knot View Template|
image = IstanbulFloorMosaic.jpg |
text = A mosaic seen on an Istanbul floor}}
|
{{Knot View Template|
image = Jaromer-Czech-CoA.png |
text = Coat of arms of Jaroměř, Czech Republic}}
|- valign=top
{{Knot View Template|
image = St-Savior-Jersey-UK-COA.gif |
text = Coat of arms of St. Savior, Jersey, Channel Islands, depicting Crown of Thorns religious symbol}}
|
{{Knot View Template|
image = Sameba Cathedral Tbilisi 13.jpg |
text = Cathedral in Tbilisi, Georgia}}
|
{{Knot View Template|
image = Mozota-Coatofarms.gif |
text = Coat of arms of Mozota, Spain}}
|
{{Knot View Template|
image = Decorative motif of interlaced squares, San Pancrazio, Florence.jpg |
text = Decorative motif of interlaced squares, San Pancrazio, Florence}}
|- valign=top
{{Knot View Template|
image = Macedonian cross.png |
text = Macedonian cross}}
|
{{Knot View Template|
image = 8crossings-link-3D.PNG |
text = 3D depiction}}
|
{{Knot View Template|
image = Visitacao Braga Brazao.jpg |
text = ''Arma Christi'' carving in monastery in Portugal}}
|
{{Knot View Template|
image = Handewitt Schleswig-Holstein arms oak.png |
text = Handewitt, Schleswig-Holstein oak leaves and acorns}}
|
|- valign=top
{{Knot View Template|
image = Onam festival flower carpet Maspraveen.jpg |
text = Flower carpet, south India}}
|
{{Knot View Template|
image = Flower carpet onam . irvin 01.jpg |
text = Flower carpet, south India}}
|
{{Knot View Template|
image = Persian or central Asian tile detail 15th century.JPG |
text = Islamic art tile}}

|
{{Knot View Template|
image = 8crossingsmarocco.jpg |
text = moroccan craft}}

{{Knot View Template|
image = Murato.jpg |
text = Link on a church of Murato,Corsica }}

|}

File:Murato.jpg

2018-06-04T09:34:45Z

Robert FERREOL: link, church of Murato, Corsica

link, church of Murato, Corsica

7 4 Further Notes and Views

2018-02-16T06:39:53Z

Robert FERREOL: adding raelian logo

File:Symboleraelien.jpg

2018-02-16T06:37:17Z

Robert FERREOL:

7 4 Further Notes and Views

2018-02-16T06:36:31Z

Robert FERREOL:

<noinclude>Back to [[7_4]].</noinclude>
{|
|- valign=top
{{Knot View Template|
image = Celtic-knot-linear-7crossings.png |
text = Celtic or pseudo-Celtic knot}}
{{Knot View Template|
image = mongolian74.gif |
text = Mongolian ornament}}
{{Knot View Template|
image = SusanWilliamsMedallion_160.jpg |
text = Susan Williams' medallion [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/SusanWilliamsMedallion.html], the "Endless knot" of Buddhism [http://en.wikipedia.org/wiki/Endless_knot]}}

{{Knot View Template|
image = Endless knot outlined.png |
text = Ornamental "Endless knot"}}
|- valign=top
{{Knot View Template|
image = KornikKnot_160.jpg |
text = a knot seen at the Castle of Kornik [http://www.math.toronto.edu/~drorbn/Gallery/KnottedObjects/KornikKnot.html]}}
{{Knot View Template|
image = Takara-4harts-C7.jpg |
text = A 7-4 knot reduced from TakaraMusubi with 9 crossings
[http://intervision.aadau.net/]}}

{{Knot View Template|
image = TakaraMusubi-C9.jpg |
text = TakaraMusubi knot seen in Japanese symbols, or Kolam in South India
[http://intervision.aadau.net/]}}

{{Knot View Template|
image = Ashtamangala-Endless-knot.jpg |
text = Buddhist Endless Knot}}
|- valign=top
{{Knot View Template|
image = Endless-knot-Shrivatsa.jpg |
text = Ornamental Endless Knot}}

{{Knot View Template|
image = Duerer-knot.jpg |
text = Albrecht Dürer knot, 16th-century}}
{{Knot View Template|
image = LaserCut_7_4_120.jpg |
text = A laser cut by Tom Longtin [http://mysite.verizon.net/t.longtin/knot_atlas/index.html]}}

{{Knot View Template|
image = Interwoven unicursal hexagram.gif |
text = Unicursal hexagram of occultism}}
|- valign=top
{{Knot View Template|
image = p11.gif |
text = Lissajous curve : x=cos 3t , y=sin 2t, z=sin 7t}}

{{Knot View Template|
image = symboleraelien.jpg |
text = logo of the raelian sect}}

|}

L9a33 Further Notes and Views

2018-01-01T21:01:58Z

Robert FERREOL: adding a picture

<noinclude>Back to [[L9a33]].</noinclude>
<br>
{|
|- valign=top
{{Knot View Template|
image = L9a33-symm-circ-arcs.png|
text = Symmetric form}}
|
{{Knot View Template|
image = L9a33-symm-circ-arcs-alt.png|
text = Alternate symmetric version, with three lines touching at center}}
|
{{Knot View Template|
image = L9a33-symm-circ-arcs-7enclosed.png|
text = Alternate symmetric version, with three lines touching at circumference}}
|- valign=top
{{Knot View Template|
image = Link9-corners.png |
text = Form made from 45-degree lines and circular arcs.}}
|
{{Knot View Template|
image = Acdeicjb.png |
text = Depiction obtained by knotilus.}}
|
{{Knot View Template|
image = Oddcnlclmfplejdg.png |
text = With an hypotrochoid [http://www.mathcurve.com/courbes2d/hypotrochoid/hypotrochoid.shtml].}}
|
{{Knot View Template|
image = 2017-12-07_10.44.34.jpg|
text = Mexican book.}}

|}

File:2017-12-07 10.44.34.jpg

2018-01-01T20:59:17Z

Robert FERREOL: Mexican book

Mexican book