Apeirohedron

An apeirohedron is a polyhedron having infinitely many faces. Like an ordinary polyhedron it forms a surface with no border. But where an ordinary polyhedral surface has no border because it folds round to close back on itself, an apeirohedron has no border because its surface is unbounded.

Two main types have been studied:
*Tilings or tessellations of the plane.
*Skew polyhedra filling 3-space.

Apeirotope

In general, an "n-apeirotope" is an infinite n-polytope. Again there are two main classes studied: tessellations of (n-1)-space, or "skew" forms in n-space.

For example the convex uniform honeycombs are uniform "4-apeirotopes" tessellating 3-space.

ee also

*Apeirogon

References

* Peter McMullen, Egon Schulte, Abstract Regular Polytopes, Cambridge University Press, 2002. ISBN 0-521-81496-0 (Page 25)