Orthogonal Polyhedra

The following polyhedra are composed of cubes glued together, whose surface is then triangulated. (The triangulation is not shown below, but there are vertices at all cube corners, even if collinear or coplanar.)
All times were measured on on an SGI R50000 (200 MHZ) with 128MB RAM.

All images Copyright (C) 2000 Biliana Kaneva and Joseph O'Rourke and Veronica Morales

An orthogonal polyhedron of 20 vertices composed of four cubes (36 faces).

Statistics: n = 20; F = 36; time = 1.022 sec; memory = 0.903 Mb
An orthogonal torus composed of 8 cubes (32 vertices, 64 faces).

Statistics: n = 32; F = 64; time = 2 sec; memory = 1.86 Mb
An orthogonal polyhedron built from 27 cubes (108 vertices, 216 faces).
(This is the polyhedron featured in Fig. 4.22 p.154 of Computational Geometry in C [2nd Ed.]).

Statistics: n = 108; F = 216; time = 10 sec; memory = 6.15 Mb
An orthogonal polyhedron of 400 vertices composed of 99 cubes (796 faces).
(This is the polyhedron featured in Fig. 7.10 p.251 of Computational Geometry in C [2nd Ed.]).

Statistics: n = 400; F = 796; time = 86 sec; memory = 24.89 Mb
An orthogonal polyhedron 440 vertices composed of 111 cubes (876 faces).

Statistics: n = 440; F = 876; time = 62 sec; memory = 19.16 Mb

Research supported by NSF grant CCR-9731804.
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