Convex uniform 5-polytopes

Importance: Medium ✭✭
Subject: Geometry
Recomm. for undergrads: yes
Posted by: ACW
on: May 24th, 2012

\begin{problem} Enumerate all convex uniform 5-polytopes. \end{problem}

% You may use many features of TeX, such as % arbitrary math (between $...$ and $$...$$) % \begin{theorem}...\end{theorem} environment, also works for question, problem, conjecture, ... % % Our special features: % Links to wikipedia: \Def {mathematics} or \Def[coloring]{Graph_coloring} % General web links: \href [The On-Line Encyclopedia of Integer Sequences]{} A reasonably complete discussion, with a list of all known examples, is at \Def{Uniform_5-polytope}. The known examples form two infinite classes and 105 additional examples. All the known examples but one are "Wythoffian", and any unknown examples must be non-Wythoffian. The proposer believes that a talented undergraduate could put this to rest.


% Example: %*[B] Claude Berge, Farbung von Graphen, deren samtliche bzw. deren ungerade Kreise starr sind, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 10 (1961), 114. % %[CRS] Maria Chudnovsky, Neil Robertson, Paul Seymour, Robin Thomas: \arxiv[The strong perfect graph theorem]{math.CO/0212070}, % Ann. of Math. (2) 164 (2006), no. 1, 51--229. \MRhref{MR2233847} % % (Put an empty line between individual entries)

* indicates original appearance(s) of problem.