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File:Circular-cross-decorative-knot-12crossings.svg

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Description

Decorative knot with twelve crossings, depicted with four-fold symmetry, and having an overall interlaced quasi-cross shape inside an enclosing circle. This is a variant of File:12crossings-fourfold-symmetric.svg (which has all knot crossings at 90° angles), and is topologically equivalent to File:12crossings-4symmetrical-square.svg (see http://katlas.math.toronto.edu/wiki/K12a975 ).

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Self-made graphic, converted from the following vector PostScript source code:

%!
306 396 translate 1.1 -1.1 scale 38.75 setlinewidth/X{972 sqrt
10 add 3 sqrt mul 118 add}def/W{30000 sqrt 10 sub}def/Z{X 72
sub}def X neg 0 36 180 300 arc 0 W neg 200 120 60 arcn
X 0 36 240 0 arc 0 0 X 36 add 0 90 arc
0 X 36 90 210 arc W neg 0 200 30 330 arcn
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X 0 36 0 120 arc 0 W 200 300 240 arcn
X neg 0 36 60 180 arc 0 0 X 36 add 180 270 arc
0 X neg 36 270 30 arc W 0 200 210 150 arcn
0 X 36 -30 90 arc 0 0 X 36 add 90 180 arc closepath
gsave 50 setlinewidth 1 .9 1 setrgbcolor stroke grestore stroke
4{50 setlinewidth 1 .9 1 setrgbcolor
0 W neg 200 91 109 arc stroke 
X 0 36 85 0 arcn 0 0 X 36 add 360 343.5 arcn stroke 
0 W 200 247 240 arcn -50 dup 3 sqrt div neg rlineto stroke 
38.75 setlinewidth 0 setgray 0 W neg 200 90 110 arc stroke 
X 0 36 86 0 arcn 0 0 X 36 add 360 342.5 arcn stroke
0 W 200 248 240 arcn -52 dup 3 sqrt div neg rlineto stroke 
90 rotate}repeat showpage
%EOF
Author AnonMoos
Other versions

For a quasi-version of this with threefold symmetry (i.e. 9 crossings) see File:9crossings-decorative-knot-threefold-incircle.svg .

For a 12-crossing knot with three-fold symmetry, see File:12crossings-rose-rhodonea-limacon-symmetrical-knot.svg and for a 12-crossing knot with two-fold symmetry, see File:12crossings-rose-limacon-knot.svg .

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05dd0d380a8087d6eeefe913eb49ff3ded8bc324

4,094 byte

600 pixel

600 pixel

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Date/TimeThumbnailDimensionsUserComment
current16:56, 2 August 2010Thumbnail for version as of 16:56, 2 August 2010600 × 600 (4 KB)AnonMoos== {{int:filedesc}} == Decorative knot with twelve crossings, depicted with four-fold symmetry, and having an overall interlaced quasi-cross shape inside an enclosing circle. This is a variant of File:12crossings-fourfold-symmetric.svg and topologic

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