## Convex Polytopes: Spheres

Below are polytopes of
approximately n = 1000, 4000, 7000, and 8000 vertices
on a sphere,
each with all the shortest paths drawn
from a particular source point to all vertices.
The source point is not visible in the images, as we chose
to show the "backside" of the polytopes, where the paths
are more clearly distinguished.

All times were measured on on an Linux PC with a Pentium III 600 MHz processor
and 256MB RAM.
All images Copyright (C) 2000 Biliana Kaneva and Joseph O'Rourke

A polytope of approx. 1,000 vertices on
the surface of a sphere (2,000 faces).

Statistics:
n = 995;
F = 1986;
time = 11 sec;
memory = 10.43 MB

A polytope of approx. 4,000 vertices on
the surface of a sphere (8,000 faces).

Statistics:
n = 3724; F = 7444;
time = 205 sec;
memory = 60.849 MB

A polytope of approx. 7,000 vertices on
the surface of a sphere (14,000 faces).

Statistics:
n = 6551; F = 13098;
time = 1008 sec;
memory = 141.503 MB

A polytope of approx. 8,000 vertices on
the surface of a sphere (16,000 faces).

Statistics:
n = 7660; F = 15316;
time = 1620 sec;
memory = 179.226 MB

Research supported by NSF grant CCR-9731804.

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