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Apeirotope

An apeirotope is a polytope with infinitely many elements.[1] The most common examples of these are tilings or honeycombs. This term is almost always used exclusively for polytopes with countably many elements, as any (strongly connected) polytope must have countably many elements.

The hyperbolic tiling order-6 pentagonal tiling is an apeirohedron.

The apeirogon is the unique[note 1] connected apeirotopic polygon.

Notes edit

  1. ↑ Unique up to abstract equivalence.

References edit

  1. ↑ McMullen, Peter (1994). "Realizations of regular apeirotopes". Aequationes Mathematicae. 47 (2–3): 223–239. doi:10.1007/BF01832961. MR 1268033.
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