Tight orientably-regular polytopes
Abstract
It is known that every equivelar abstract polytope of type {p1, …, pn − 1} has at least 2p1⋯pn − 1 flags. Polytopes that attain this lower bound are called tight. Here we investigate the conditions under which there is a tight orientably-regular polytope of type {p1, …, pn − 1}. We show that it is necessary and sufficient that whenever pi is odd, both pi − 1 and pi + 1 (when defined) are even divisors of 2pi.
Keywords
Abstract regular polytope, equivelar polytope, flat polytope, tight polytope
DOI: https://doi.org/10.26493/1855-3974.554.e50
ISSN: 1855-3974
Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications