Gallery¶

Table 2 GC Operation¶
_images/geodesic_8.png

A standard (method 1) 8-frequency geodesic division of an icosahedron. gcopoly.py icosahedron.off -a 8 | off_color -f C | antiview -R 90,0,0

_images/cube_4_3.png

(4,3) GC operation on a cube, in canonical form. gcopoly.py cube.off -a 4 -b 3 | canonical | off_color -f C| antiview -R 90,0,0

_images/tet_5_3.png

Standard (method 1) (5,3) subdivision of a tetrahedron. (Notice the vertices in the upper left and lower right.) gcopoly.py tetrahedron.off -a 5 -b 3 | off_color -f G | antiview -R 90,0,0

_images/tet_5_3_opt.png

(5,3) subdivision of a tetrahedron, but using nslerp projection and optimized to reduce variation in face area. gcopoly.py tetrahedron.off -a 5 -b 3 -p nslerp -k faces | off_color -f G | antiview -R 90,0,0

_images/cellular.gif

Conway’s Game of Life on the surface of a (5,3) subdivided cube. Courtesy of Roger Kaufman.

_images/virus_1.png

Repeatedly applying the (1,1) triangular subdivision using the flat projection and not normalizing gives this interesting organic shape. It resembles a viral capsid (moreso than geodesic polyhedra usually resemble a viral capsid), or a strange fruit. Produced by gcopoly.py icosahedron.off -a 9 -n -f |antiview: -a 7 and -a 5 -b 3 are similar.

_images/3di.png

Improper geodesic polyhedron on the 3-dihedron. Note dangling faces. gcopoly.py 4dihedron.off -a 5 -b 3 -p nslerp -k energy | off_color -f C | antiview -R 90,90,0

_images/4di.png

GC operation on the 4-dihedron. gcopoly.py 4dihedron.off -a 5 -b 3 -p nslerp -k energy | off_color -f C | antiview -R 90,45,0

Table 3 Other scripts¶
_images/breakdown_4_4_nslerp2.png

Quadrilateral nslerp2 preserves diagonal lines across the face. breakdown.py 4 4 -q -p=nslerp2

_images/breakdown_4_4_disk.png

An attractive floral pattern produced by breakdown.py 4 4 -z 0 -q -p=disk

_images/balloon_10.svg

A triangular balloon polyhedron. balloon.py 10 | off_color -f C | view_off.py -e 0 -d 5.5

_images/balloon_10_qpl.svg

A quadrilateral balloon polyhedron, which resembles the shape of a peeled coconut. balloon.py 10 -q -p -l | off_color -f C | view_off.py -d 5.6 -e 0

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Contents:

  • Goldberg-Coxeter Operations on Polyhedra and Tilings
  • Gallery
  • Modules and scripts

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  • Documentation overview
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