Regular Polygonal Complexes of Higher Ranks in $\mathbb{E}^3$

Egon Schulte

Northeastern University, Department of Mathematics, 360 Huntington Avenue, Boston, MA 02115, USA

Abstract: The paper establishes that the rank of a regular polygonal complex in $\mathbb{E}^3$ cannot exceed $4$, and that the only regular polygonal complexes of rank $4$ in $\mathbb{E}^3$ are the eight regular $4$-apeirotopes in $\mathbb{E}^3$.
The article is published in the author's wording.

Keywords: polygonal complex, abstract polytopes, regularity.

UDC: 514.113.5

Received: 15.10.2013

Language: English