✦ LIBER ✦

Realizations of regular polytopes

✍ Scribed by Peter McMullen

Publisher: Springer
Year: 1988
Tongue: English
Weight: 54 KB
Volume: 36
Category: Article
ISSN: 0001-9054
DOI: 10.1007/bf01836099

No coin nor oath required. For personal study only.

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We define incidence quasi-polytopes and give a procedure for constructing regular incidence quasi-polytopes. We use this procedure to construct a finite map of type {e, 6} for all even ~ and 6, and infinitely many such maps when ~ or 6 is divisible by 4 and both are greater than or equal to 4.

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It is shown that under certain conditions the regularization of a pair of regular incidence polytopes is not itself an incidence polytope. Thus there exist regular incidence quasipolytopes which are not incidence polytopes.