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File:Asymptote Diagrams of Four Semiplanigons.png

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English: A diagram illustrating circle inscription in each of the four semiplanigons, V3.3.4.12, V3.4.3.12, V3.3.6.6, and V3.4.4.6. Small and big vertex polygons are present, with small vertex polygons inscribed in the circles. This was made in Asymptote (vector graphics language) and is a vector graphic.
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Source Own work
Author Harry Princeton

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Code Used in Asymptote Can be reproduced with credit to me. Tomruen: do not copy or attempt to use your own version!

[asy] filldraw((0,0)--(0,224/40)--(-52/40,254/40)--(-123/40,213/40)--cycle,rgb(0.0,1.0,1.0),rgb(0.0,0.5,0.5)); filldraw(circle((-52/40,194/40),52/40),rgb(0.0,0.875,0.875)); filldraw((0,194/40)--(-26/40,239/40)--(-78/40,239/40)--(-97/40,168/40)--cycle,rgb(0.0,0.8,0.8),rgb(0.0,0.75,0.75)); draw((-52/40,194/40)--(52/40,194/40),gray); draw((-52/40,194/40)--(0,284/40),gray); draw((-52/40,194/40)--(-104/40,284/40),gray); draw((-52/40,194/40)--(-142/40,142/40),gray); dot((-52/40,194/40)); draw((52/40,194/40)--(142/40,142/40)--(194/40,52/40),rgb(0.75,0.75,0.75)+dashed); draw((-142/40,142/40)--(-194/40,52/40),rgb(0.75,0.75,0.75)+dashed); draw((-142/40,142/40)--(-194/40,232/40)--(-104/40,284/40)--(0,284/40)--(52/40,194/40),rgb(0.75,0.75,0.75)+dashed); draw((52/40,194/40)--(0,284/40)--(-104/40,284/40)--(-142/40,142/40)--cycle,rgb(0.0,0.625,0.625)+dashed); add(pathticks((-52/40,194/40)--(0,194/40),1,0.5,0,390/40)); add(pathticks((0,194/40)--(52/40,194/40),1,0.5,0,390/40)); add(pathticks((-52/40,194/40)--(-26/40,239/40),1,0.5,0,390/40)); add(pathticks((-26/40,239/40)--(0,284/40),1,0.5,0,390/40)); add(pathticks((-52/40,194/40)--(-78/40,239/40),1,0.5,0,390/40)); add(pathticks((-78/40,239/40)--(-104/40,284/40),1,0.5,0,390/40)); add(pathticks((-52/40,194/40)--(-97/40,168/40),1,0.5,0,390/40)); add(pathticks((-97/40,168/40)--(-142/40,142/40),1,0.5,0,390/40)); draw(rightanglemark((-142/40,142/40),(-97/40,168/40),(-123/40,213/40))); draw(rightanglemark((-123/40,213/40),(-78/40,239/40),(-104/40,284/40))); draw(rightanglemark((0,224/40),(-26/40,239/40),(0,284/40))); draw(rightanglemark((0,224/40),(0,194/40),(52/40,194/40))); draw((0,0)--(0,224/40)--(-52/40,254/40)--(-123/40,213/40)--cycle,rgb(0.0,0.5,0.5)); draw(circle((-52/40,194/40),52/40)); label("Circle in semiplanigon \textcolor[rgb]{0.0,0.5,0.5}{V$3^2.4.12$}.",(-52/40,-30/40)); [/asy] [asy] pair A,B,C,D,E,F,G,H,I,J,K,L,M,N; A=(-52/40,-52/40); B=(-52/40,52/40); C=(52/40,-52/40); D=(52/40,52/40); E=(0,142/40); F=(142/40,0); G=(0,246/40); H=(52/40,336/40); I=(246/40,0); J=(336/40,52/40); K=(A+B+C+D)/4; L=(B+D+E)/3; M=(C+D+F)/3; N=(194/40,194/40); filldraw(K--L--N--M--cycle,rgb(1.0,1.0,0.0),rgb(0.5,0.5,0.0)); filldraw(circle(D,52/40),rgb(0.875,0.875,0)); filldraw((B+D)/2--(C+D)/2--(D+F)/2--(D+E)/2--cycle,rgb(0.8,0.8,0.0),rgb(0.75,0.75,0.0)); draw(D--B,gray); draw(D--C,gray); draw(D--F,gray); draw(D--E,gray); dot(D); draw(J--I--F--C--A--B--E--G--H,rgb(0.75,0.75,0.75)+dashed); draw(B--C--F--E--cycle,rgb(0.625,0.625,0.0)+dashed); add(pathticks(D--(B+D)/2,1,0.5,0,390/40)); add(pathticks(B--(B+D)/2,1,0.5,0,390/40)); add(pathticks(D--(C+D)/2,1,0.5,0,390/40)); add(pathticks(C--(C+D)/2,1,0.5,0,390/40)); add(pathticks(D--(F+D)/2,1,0.5,0,390/40)); add(pathticks(F--(F+D)/2,1,0.5,0,390/40)); add(pathticks(D--(E+D)/2,1,0.5,0,390/40)); add(pathticks(E--(E+D)/2,1,0.5,0,390/40)); draw(rightanglemark(K,(B+D)/2,B)); draw(rightanglemark(K,(C+D)/2,C)); draw(rightanglemark(N,(E+D)/2,E)); draw(rightanglemark(N,(F+D)/2,F)); draw(circle(D,52/40)); label("Circle in semiplanigon \textcolor[rgb]{0.5,0.5,0.0}{V$3.4.3.12$}.",(52/40,-82/40)); [/asy] [asy] pair A,B,C,D,E,F,G,H,I,J,K,L,M; A=(104/40,0); B=(52/40,90/40); C=(52/40,-90/40); D=(0,0); E=(0,180/40); F=(0,-180/40); G=(-104/40,180/40); H=(-104/40,-180/40); I=(-52/40,90/40); J=(-52/40,-90/40); K=(A+B+D)/3; L=(A+C+D)/3; M=(-104/40,0); filldraw(I--J--L--K--cycle,rgb(1.0,0.0,1.0),rgb(0.5,0.0,0.5)); filldraw(circle(D,52/40),rgb(0.875,0.0,0.875)); filldraw((B+D)/2--(A+D)/2--(C+D)/2--(M+D)/2--cycle,rgb(0.8,0.0,0.8),rgb(0.75,0.0,0.75)); draw(D--B,gray); draw(D--A,gray); draw(D--C,gray); draw(D--M,gray); dot(D); draw(G--E--A--F--H,rgb(0.75,0.75,0.75)+dashed); draw(B--A--C--M--cycle,rgb(0.625,0.0,0.625)+dashed); add(pathticks(D--(B+D)/2,1,0.5,0,390/40)); add(pathticks(B--(B+D)/2,1,0.5,0,390/40)); add(pathticks(D--(A+D)/2,1,0.5,0,390/40)); add(pathticks(A--(A+D)/2,1,0.5,0,390/40)); add(pathticks(D--(C+D)/2,1,0.5,0,390/40)); add(pathticks(C--(C+D)/2,1,0.5,0,390/40)); add(pathticks(D--(M+D)/2,1,0.5,0,390/40)); add(pathticks(M--(M+D)/2,1,0.5,0,390/40)); draw(rightanglemark(A,(A+D)/2,C)); draw(rightanglemark(B,(B+D)/2,I)); draw(rightanglemark(C,(C+D)/2,J)); draw(rightanglemark(M,(M+D)/2,J)); draw(circle(D,52/40)); label("Circle in semiplanigon \textcolor[rgb]{0.5,0.0,0.5}{V$3^2.6^2$}.",(0,-210/40)); [/asy] [asy] pair A,B,C,D,E,F,G,H,I,J,K,L,M; A=(-104/40,0); B=(0,-104/40); C=(104/40,0); D=(0,0); E=(52/40,90/40); F=(0,180/40); G=(-104/40,180/40); H=(-104/40,-104/40); I=(104/40,-104/40); J=(-52/40,90/40); K=(A+B+D+H)/4; L=(B+C+D+I)/4; M=(C+D+E)/3; filldraw(J--K--L--M--cycle,rgb(0.5,0.5,1.0),rgb(0.0,0.0,1.0)); filldraw(circle(D,52/40),rgb(0.375,0.375,1.0)); filldraw((A+D)/2--(B+D)/2--(C+D)/2--(E+D)/2--cycle,rgb(0.3,0.3,1.0),rgb(0.25,0.25,1.0)); draw(D--A,gray); draw(D--B,gray); draw(D--C,gray); draw(D--E,gray); dot(D); draw(A--H--I--C--F--G,rgb(0.75,0.75,0.75)+dashed); draw(A--B--C--E--cycle,rgb(0.125,0.125,1.0)+dashed); add(pathticks(D--(A+D)/2,1,0.5,0,390/40)); add(pathticks(A--(A+D)/2,1,0.5,0,390/40)); add(pathticks(D--(B+D)/2,1,0.5,0,390/40)); add(pathticks(B--(B+D)/2,1,0.5,0,390/40)); add(pathticks(D--(C+D)/2,1,0.5,0,390/40)); add(pathticks(C--(C+D)/2,1,0.5,0,390/40)); add(pathticks(D--(E+D)/2,1,0.5,0,390/40)); add(pathticks(E--(E+D)/2,1,0.5,0,390/40)); draw(rightanglemark(A,(A+D)/2,J)); draw(rightanglemark(B,(B+D)/2,K)); draw(rightanglemark(C,(C+D)/2,M)); draw(rightanglemark(E,(E+D)/2,J)); draw(circle(D,52/40)); label("Circle in semiplanigon \textcolor[rgb]{0.0,0.0,1.0}{V$3.4^2.6$}.",(0,-134/40)); [/asy]

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Date/TimeThumbnailDimensionsUserComment
current23:57, 15 July 2019Thumbnail for version as of 23:57, 15 July 201910,000 × 2,240 (517 KB)Harry Princeton (talk | contribs)Cross-wiki upload from en.wikipedia.org

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