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| View Original: | Trefoil-non-3-symm-flip demonstration.svg (800x416) | |||
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| Keywords: Trefoil-non-3-symm-flip demonstration.svg Knot transformation diagram to demonstrate that the form of the trefoil knot depicted without visible three-fold structure as seen at lower left i e File Trefoil-non-3-symm svg is topologically equivalent to the more usual form of the trefoil knot seen at upper left i e a triquetra shape In order to show this the lower left looping of the knot is flipped over in the third dimension to the upper left area removing one crossing and creating one new crossing Trefoil-non-3-symm svg Self-made graphic converted from the following vector PostScript source code <pre> 310 396 translate 775 dup scale/z 20000 sqrt def 92 96 1 setrgbcolor 12 setlinewidth/A z 0 100 225 270 arc z Q add -100 lineto z Q add 100 lineto 0 0 100 90 135 arc z -2 div 50 add z 5 mul neg 50 add 100 135 195 arc z neg 50 add 50 100 255 315 arc z 50 sub -50 100 135 def/B -10 10 moveto 20 -20 rlineto stroke 0 0 100 126 135 arc -11 -11 rlineto stroke def/C -11 11 moveto 22 -22 rlineto stroke 0 0 100 125 135 arc -12 -12 rlineto stroke def gsave -200 0 translate 0 0 100 315 270 arcn z 30 add neg -100 lineto z 30 add neg 100 lineto z neg 0 100 90 45 arcn/Q 30 def A 75 arcn z 2 div 50 sub z 2 div 50 sub 100 15 -45 arcn closepath gsave 0 setgray 32 setlinewidth stroke grestore stroke 0 setgray 32 setlinewidth B 0 0 100 306 315 arc 11 11 rlineto stroke 92 96 1 setrgbcolor 12 setlinewidth C 0 0 100 305 315 arc 12 12 rlineto stroke grestore gsave 180 0 translate 0 z 100 180 225 arc/Q 40 def A 90 arcn z 50 sub 150 100 270 285 arc 46 593 124 1181 100 -45 0 arc 46 593 150 100 0 90 arc -100 250 lineto closepath gsave 0 setgray 32 setlinewidth stroke grestore stroke 0 setgray 32 setlinewidth B 46 593 124 1181 100 -27 -7 arc stroke 92 96 1 setrgbcolor 12 setlinewidth C 46 593 124 1181 100 -28 -6 arc stroke grestore gsave -270 187 5 translate 25 dup scale 1 setlinejoin 1 96 92 setrgbcolor 30 setlinewidth/x 240 3 sqrt div neg def/y x 120 3 sqrt mul add def 0 x 240 0 180 arc -120 y 240 -120 60 arc 120 y 240 120 300 arc closepath gsave 0 setgray 80 setlinewidth stroke grestore stroke 0 setgray 80 setlinewidth -120 y 240 -15 16 arc stroke 0 x 240 105 136 arc stroke 120 y 240 225 256 arc stroke 1 96 92 setrgbcolor 30 setlinewidth -120 y 240 -16 17 arc stroke 0 x 240 104 137 arc stroke 120 y 240 224 257 arc stroke grestore 1 0 0 setrgbcolor 46 setlinewidth -5 133 92 180 90 arcn stroke -10 267 moveto -10 183 lineto 32 225 lineto closepath fill showpage EOF</pre> Trefoil knots Images with PostScript source code Knots and links on transparent background Outline knots and links | ||||
