Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,2,36}

Atlas Canonical Name {8,2,36}*1152

Overview

Group
SmallGroup(1152,119743)
Rank
4
Schläfli Type
{8,2,36}
Vertices, edges, …
8, 8, 36, 36
Order of s0s1s2s3
72
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

8-fold

9-fold

12-fold

16-fold

18-fold

24-fold

36-fold

48-fold

72-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11)(12,13)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28)(29,30)(31,34)(32,33)(35,36)(37,38)(39,42)(40,41)(43,44);;
s3 := ( 9,15)(10,12)(11,21)(13,23)(14,17)(16,19)(18,29)(20,31)(22,25)(24,27)(26,37)(28,39)(30,33)(32,35)(34,43)(36,40)(38,41)(42,44);;
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, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(44)!(2,3)(4,5)(6,7);
s1 := Sym(44)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(44)!(10,11)(12,13)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28)(29,30)(31,34)(32,33)(35,36)(37,38)(39,42)(40,41)(43,44);
s3 := Sym(44)!( 9,15)(10,12)(11,21)(13,23)(14,17)(16,19)(18,29)(20,31)(22,25)(24,27)(26,37)(28,39)(30,33)(32,35)(34,43)(36,40)(38,41)(42,44);
poly := sub<Sym(44)|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, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;