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DeutschFile:Double six.svg
Size of this PNG preview of this SVG file: 622 × 599 pixels. Other resolutions: 249 × 240 pixels | 498 × 480 pixels | 797 × 768 pixels | 1,063 × 1,024 pixels | 2,125 × 2,048 pixels | 635 × 612 pixels.
Original file (SVG file, nominally 635 × 612 pixels, file size: 14 KB)
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Summary
| Description | English: Schläfli's double six configuration — twelve lines with five intersection points per line and two lines per intersection point, intersecting in the pattern of a crown graph — inscribed on a cube, following an illustration by Hilbert and Cohn-Vossen in Geometry and the Imagination. |
| Date | |
| Source | Own work |
| Author | David Eppstein |
| Other versions |  |
Source code
The basic geometry of this image was created with the following Python script (much of which was copied from the one used for File:Gray configuration.svg). The transparency effects were added afterwards, using Adobe Illustrator.
from pyx import canvas,path,color from math import sqrt,tan,asin pov = (-22.7,7.1,9.3) x,y,z = 2,1,0 radius = 0.12 scale = 10.0 g = 2.0 h = 2.5 vertexColor = [color.rgb.red] edgeColor = [color.rgb.black] cubeColor = [color.rgb.blue] def distance(p,q): return sqrt(sum([(p[i]-q[i])**2 for i in (x,y,z)])) def perspective(loc): dz = loc[z]-pov[z] return (loc[x]-pov[x])*scale/dz, (loc[y]-pov[y])*scale/dz def vertex(p): lx,ly = perspective(p) prad = scale*1.1*tan(asin(radius/(distance(p,pov)))) c.fill(path.circle(lx,ly,prad),vertexColor) def edge(p,q): lx1,ly1 = perspective(p) lx2,ly2 = perspective(q) c.stroke(path.line(lx1,ly1,lx2,ly2),edgeColor) def cube(p,q): lx1,ly1 = perspective(p) lx2,ly2 = perspective(q) c.stroke(path.line(lx1,ly1,lx2,ly2),cubeColor) c = canvas.canvas() def transform(point,spin,flip,mirror,turn): x,y,z = point if mirror: x,y,z = y,x,z if turn: x,y,z = -x,-y,z if flip: x,y,z = -y,x,-z for i in range(spin): x,y,z = y,z,x return x,y,z points = set() lines = set() for s in (0,1,2): for f in (0,1): points.add(transform((0,0,g),s,f,0,0)) for m in (0,1): for t in (0,1): points.add(transform((g,g/h,g),s,f,m,t)) points.add(transform((g*h,g,g),s,f,m,t)) lines.add((transform((g*h,g,g),s,f,m,0), transform((-g*h,-g,g),s,f,m,0))) for a in (-2,2): for b in (-2,2): cube((a,b,-2),(a,b,2)) cube((a,-2,b),(a,2,b)) cube((-2,a,b),(2,a,b)) for p,q in lines: edge(p,q) for p in points: vertex(p) c.writePDFfile("Double_six") Licensing
 | I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:59, 3 January 2017 | | 635 × 612 (14 KB) | Hedwig in Washington | Reverted to version as of 23:29, 31 July 2010 (UTC) |
| 23:29, 31 July 2010 |  | 635 × 612 (14 KB) | David Eppstein | {{Information |Description={{en|1=Schläfli's double six configuration — twelve lines with five intersection points per line and two lines per intersection point, intersecting in the pattern of a crown graph — inscribed on a cube, |
File usage
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Global file usage
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