login
This site is supported by donations to The OEIS Foundation.

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A141536 Orders, sorted, of embeddable Wythoffians in dimension 4. 0

%I

%S 5,8,16,10,30,64,120,192,384,1152,14400

%N Orders, sorted, of embeddable Wythoffians in dimension 4.

%C Sorted from Deza et al., Table 2, p.5. Abstract: The Wythoff construction takes a d-dimensional polytope P, a subset S of {0, . . ., d} and returns another d-dimensional polytope P(S). If P is a regular polytope, then P(S) is vertex-transitive. This construction builds a large part of the Archimedean polytopes and tilings in dimension 3 and 4. We want to determine, which of those Wythoffians P(S) with regular P have their skeleton or dual skeleton isometrically embeddable into the hypercubes H_m and half-cubes (1/2)H_m. We find six infinite series, which, we conjecture, cover all cases for dimension d > 5 and some sporadic cases in dimension 3 and 4 (see Tables 1 and 2).

%C Three out of those six infinite series are explained by a general result about the embedding of Wythoff construction for Coxeter groups. In the last section, we consider the Euclidean case; also, zonotopality of embeddable P(S) are addressed throughout the text.

%H Michel Deza, Mathieu Dutour and Sergey Shpectorov, <a href="http://arxiv.org/abs/math/0407527">Hypercube embedding of Wythoffians</a> arXiv:math/0407527 v5, Aug 11, 2008.

%K fini,full,nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 12 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified July 30 15:34 EDT 2014. Contains 245069 sequences.