Part of the Atlas of Small Regular Polytopes

Polytope of Type {9,2,28}

Atlas Canonical Name {9,2,28}*1008

Overview

Group
SmallGroup(1008,158)
Rank
4
Schläfli Type
{9,2,28}
Vertices, edges, …
9, 9, 28, 28
Order of s0s1s2s3
252
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

7-fold

12-fold

14-fold

21-fold

42-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(16,19)(17,18)(20,21)(22,23)(24,27)(25,26)(28,29)(30,31)(32,35)(33,34)(36,37);;
s3 := (10,16)(11,13)(12,22)(14,24)(15,18)(17,20)(19,30)(21,32)(23,26)(25,28)(27,36)(29,33)(31,34)(35,37);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(37)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(37)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(37)!(11,12)(13,14)(16,19)(17,18)(20,21)(22,23)(24,27)(25,26)(28,29)(30,31)(32,35)(33,34)(36,37);
s3 := Sym(37)!(10,16)(11,13)(12,22)(14,24)(15,18)(17,20)(19,30)(21,32)(23,26)(25,28)(27,36)(29,33)(31,34)(35,37);
poly := sub<Sym(37)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;