# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
Home > Timetable > Contribution details
PDF | XML

# The smallest regular polytopes of each rank

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

## Content

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 $[3,3,\dots,3]$).

## Place

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

More