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| View Original: | 12crossings-rose-rhodonea-limacon-symmetrical-knot.svg (620x600) | |||
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| Keywords: 12crossings-rose-rhodonea-limacon-symmetrical-knot.svg Decorative knot with twelve crossings depicted with three-fold visual symmetry The curves were generated from the polar coordinates equation r b+sin aθ which is a slight generalization of the Limaçon and Rose/rhodonea curves using parameters a 3/5 and b 3/2 If the three outermost curve segments which directly connect the three outer crossings are deleted and the lines which intersect at these three outer crossings are joined together there then you get the 9-crossing knot seen in image File Knot-9crossings-symmetrical svg If everything outside of the three next-to-outermost crossings is deleted and the lines which intersect at these three crossings are joined together there then you get the Borromean rings configuration If everything outside of the three next-to-inner crossings is deleted and the lines which intersect at these three crossings are joined together there then you get a Triquetra topologically equivalent to a Trefoil knot If everything outside of the three innermost crossings is deleted and the lines which intersect at these three crossings are joined together there then you get a form of triangle topologically equivalent to a simple circle or closed loop i e unknot Self-made graphic converted from the following vector PostScript source code <pre> 300 396 translate 75 dup scale 125 setlinewidth 1 setgray/z w lineto for stroke def/ecc 1 5 def/w /th exch def th 3 mul 5 div/x exch def x sin ecc add th cos mul x sin ecc add th sin mul def/y dup w moveto 1 add 1 def 0 y 1800 w lineto for closepath gsave 0 setgray 325 setlinewidth stroke grestore stroke 0 setgray 325 setlinewidth 16 y 44 z 188 y 232 z 316 y 344 z 488 y 528 z 616 y 644 z 788 y 832 z 916 y 944 z 1088 y 1128 z 1216 y 1244 z 1388 y 1432 z 1516 y 1544 z 1688 y 1728 z 0 125 setlinewidth 1 setgray 15 y 45 z 187 y 233 z 315 y 345 z 487 y 529 z 615 y 645 z 787 y 833 z 915 y 945 z 1087 y 1129 z 1215 y 1245 z 1387 y 1433 z 1515 y 1545 z 1687 y 1729 z showpage EOF</pre> 2010 AnonMoos For other curves generated from the polar coordinates equation r b+sin aθ see File Mathematical-polar-equation-flowers svg File Quinquetra-interlaced-alternate svg and File Interlaced-Triangles Brunnian-link alternate svg For a different decorative knot see File 12crossing-decorative-knot-triskele svg 12 crossing number knots and links Decorative knots Knot diagrams with 3-fold rotational symmetry Chiral images with rotational symmetry Images with PostScript source code Knots and links on transparent background Outline knots and links Round graphic ornaments | ||||
