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Special Topics:Tilings

DodecaFoam! Third Stellation by Chaim Goodman-Strauss and Daniel Krech

The recipe for filling a large dodecahedron with small dodecas involves examing the three stellations of the dodecahedron. Here, the third stellation of the dodecahedron is filled with tiny dodecas. Note the vertices of this figure lie on the vertices of a large dodecahedron. This symmetry is closely related to that of the three-dimensional Penrose tiles, and generalizes to dimension 4 (but no higher).

How to make it: Mathematica wrote the production rules, a program by Dan Krech iterated the rules, GeomView set up the pictures and RenderMan rendered the final result.

Image created: June 1995

[DodecaFoam!  Third Stellation]

Copyright © June 1995 by The Geometry Center, Univerity of Minnesota. All rights reserved.
For permission to use this image, contact permission@geom.umn.edu.

External viewing: small (100x100 5k gif), medium (500x494 121k gif), or original size (1720x1696 3,312k tiff).

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Created: Sat May 22 23:17:51 CDT 1999 --- Last modified: Sat May 22 23:17:51 CDT 1999