Ornamental depictions of links with 12 crossings: Difference between revisions

From Knot Atlas
Jump to navigationJump to search
No edit summary
No edit summary
 
(17 intermediate revisions by 2 users not shown)
Line 1: Line 1:
Some decorative depictions of links with 12 crossings:
Some decorative depictions of links with 12 crossings :


;I) With two component

;a) Components are loops
<gallery>
<gallery>
⚫
Image:Celtic-knot-square-3loops.png|3-loop link in the form of a quasi-Celtic knot
Image:Two-interlaced-hexagrams.png|Two interlaced open hexagrams
Image:Two-interlaced-hexagrams.png|Two interlaced open hexagrams
Image:Brunnian-3-not-Borromean.gif|Three-component [[Brunnian link]]
Image:Ccross-two-link.png|Quasi-Celtic two-loop link
⚫
Image:12crossing-twosymmetric-link.png|Two loops
⚫
Image:Brunnian-link-12crossings-nonBorromean-quasi-Arabesque.png|More ornate Brunnian link depiction
Image:Triquetra-double-interlaced.png|Two mutually-interlaced triquetras.
Image:Link12-round.png|Two loops
⚫
Image:Three-L4a1-config.png|Three-loop link with three [[L4a1]] configurations
Image:Three-L4a1.png|Two-loop link
Image:Three-L4a1.png|Two-loop link
⚫
Image:4squares-12crossings.png|Four linked squares
Image:Four-loop-interlaced-circle.png|Four-fold looping interlaced with circle (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:Ccross-two-link.png|Quasi-Celtic two-loop link
Image:Six-rings.png|Six rings
Image:Pleter50.png|Equivalent to preceding
Image:12-crossing-link Tallara Lousame Galicia Spain.jpg|Sculpture of preceding
⚫
Image:Six-link-closed-chain-Hisham-Umayyad-palace-Jericho.jpg|Decoration equivalent to a circle of six interlinked loops
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:Trefoil-in-trefoil.png|Trefoil interlinked with smaller trefoil
Image:12-crossings-squares-16.png|3-loop link in square form
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: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:12crossings-pseudo-Borromean.png|Three-loop link
Image:Triang-two-circ.png|Triangle and two circles
Image:Triang-two-circ.png|Triangle and two circles
Image:12crossings-threesymmetric-link.png|Three loops symmetric
Image:12crossings-threesymmetric-link.png|Three loops symmetric
Image:12crossings-decorative-threefold-incircle-link.png|Three loops symmetric
Image:12crossings-decorative-threefold-incircle-link.png|Three loops symmetric
Image:12crossing-twosymmetric-link.png|Two loops
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:Borromean-plus-triangle.png|Four loops (Borromean + triangle)
Image:stemariemajeure.jpg|Basilica of Saint Mary Major (not alternated)
⚫
Image:Link12-round.png|Two loops
</gallery>
Image:Two-trefoils-loop-12crossings.png|Three loops, two trefoils

Image:Two-trefoils-triangles-link.png|Two loops, two trefoils
;IV) With six loops
⚫
Image:Two-trefoils-granny-12crossings.png|Two trefoils on one loop linked with another loop
<gallery>
⚫
Image:12crossings-pseudo-Celtic-link.png|One crossing of [[K13a1345]] eliminated, converting from knot to link...
Image:Six-rings.png|Six rings
⚫
Image:12crossing-link-inrectangle.png|Two interlinked trefoils inside rectangle
⚫
Image:Six-link-closed-chain-Hisham-Umayyad-palace-Jericho.jpg|Decoration equivalent to a circle of six interlinked loops
</gallery>
</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]].
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]].

Latest revision as of 10:06, 28 April 2020

Some decorative depictions of links with 12 crossings :

I) With two component
a) Components are loops
  • Two interlaced open hexagrams

    Two interlaced open hexagrams

  • Quasi-Celtic two-loop link

    Quasi-Celtic two-loop link

  • Two loops

    Two loops

  • Two loops

    Two loops

  • Two-loop link

    Two-loop link

  • Four-fold looping interlaced with circle (two-loop link)

    Four-fold looping interlaced with circle (two-loop link)

  • Mongolian ornament, equivalent to preceding

    Mongolian ornament, equivalent to preceding

  • Equivalent to preceding

    Equivalent to preceding

  • Sculpture of preceding

    Sculpture of preceding

  • Tiling ; equivalent to preceding

    Tiling ; equivalent to preceding

  • Sicilian plate, also equivalent

    Sicilian plate, also equivalent

  • One crossing of K13a1345 eliminated, converting from knot to link...

    One crossing of K13a1345 eliminated, converting from knot to link...

b) One component is knoted
  • Two mutually-interlaced triquetras

    Two mutually-interlaced triquetras

  • Trefoil interlinked with smaller trefoil

    Trefoil interlinked with smaller trefoil

  • Two interlinked trefoils

    Two interlinked trefoils

  • Two interlinked trefoils inside rectangle

    Two interlinked trefoils inside rectangle

  • Sum of two trefoils linked with a loop

    Sum of two trefoils linked with a loop

II) With three components
  • 3-loop link in the form of a quasi-Celtic knot

    3-loop link in the form of a quasi-Celtic knot

  • Same link in this work of the Mexican artist Daniela Azuela

    Same link in this work of the Mexican artist Daniela Azuela

  • Ca. 1000 A.D. runestone, equivalent to preceding

    Ca. 1000 A.D. runestone, equivalent to preceding

  • Equivalent link in square form

    Equivalent link in square form

  • in the Greek Orthodox Church in Wien

    in the Greek Orthodox Church in Wien

  • (alternate version)

    (alternate version)

  • Three-component Brunnian link

    Three-component Brunnian link

  • More ornate Brunnian link depiction

    More ornate Brunnian link depiction

  • Three-loop link with three L4a1 configurations

    Three-loop link with three L4a1 configurations

  • Three-loop link

    Three-loop link

  • Triangle and two circles

    Triangle and two circles

  • Three loops symmetric

    Three loops symmetric

  • Three loops symmetric

    Three loops symmetric

  • Two trefoils and one loop

    Two trefoils and one loop

III) With four loops
  • Four linked squares (alternated)

    Four linked squares (alternated)

  • Variant

    Variant

  • Variant with circles

    Variant with circles

  • Variant with rectangles as an impossible object

    Variant with rectangles as an impossible object

  • Variant on the sphere ; the crossings are the vertices of the cuboctahedron

    Variant on the sphere ; the crossings are the vertices of the cuboctahedron

  • Four loops (Borromean + triangle)

    Four loops (Borromean + triangle)

  • Basilica of Saint Mary Major (not alternated)

    Basilica of Saint Mary Major (not alternated)

IV) With six loops
  • Six rings

    Six rings

  • Decoration equivalent to a circle of six interlinked loops

    Decoration equivalent to a circle of six interlinked loops

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.

Retrieved from "https://katlas.org/index.php?title=Ornamental_depictions_of_links_with_12_crossings&oldid=1724322"