Non-existence of nonorientable regular embeddings of n-dimensional cubes

By a regular embedding of a graph K into a surface we mean a 2-cell embedding of K into a compact connected surface with the automorphism group acting regularly on flags. Regular embeddings of the n-dimensional cubes Qn into orientable surfaces exist for any positive integer n. In contrast to this, we prove the non-existence of nonorientable regular embeddings of Qn for n > 2.

• Type: Journal
• Year: 2007
• Where: DM
• Authors: Young Soo Kwon, Roman Nedela
• Keywords: Compact Connected Surface, DM 2007, Nonorientable Regular Embeddings, Regular Embeddings