19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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The smallest regular polytopes of each rank

Presented by Prof. Marston CONDER
Type: Oral presentation
Track: Polytopes and Incidence Geometries


An abstract polytope is called {\em regular\/} if its automorphism group has a single orbit on flags (maximal chains). In this lecture I will report on recent work on finding for each $n$ the regular $n$-polytopes with the smallest numbers of flags. With a few small exceptions, these are also the regular $n$-polytopes with the smallest numbers of elements, and those with the smallest number of links in the Hasse diagram. Surprisingly, for $n >3$ the smallest instances are not the regular $n$-simplices (of type $[3,3,\dots,3]$).


Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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