Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,2,3,8}

Atlas Canonical Name {6,2,3,8}*1152

Overview

Group
SmallGroup(1152,157603)
Rank
5
Schläfli Type
{6,2,3,8}
Vertices, edges, …
6, 6, 6, 24, 16
Order of s0s1s2s3s4
12
Order of s0s1s2s3s4s3s2s1
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

12-fold

16-fold

24-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := ( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)(22,44)(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)(42,54)(45,46);;
s3 := ( 7,10)( 8,19)( 9,15)(12,48)(13,47)(14,31)(16,20)(17,53)(18,54)(21,46)(22,45)(23,30)(24,27)(25,26)(28,29)(33,50)(34,52)(35,39)(36,42)(37,38)(40,41)(43,44);;
s4 := ( 7,50)( 8,46)( 9,45)(10,53)(11,39)(12,40)(13,37)(14,52)(15,48)(16,30)(17,28)(18,25)(19,47)(20,27)(21,41)(22,38)(23,51)(24,49)(26,33)(29,34)(31,54)(32,42)(35,44)(36,43);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(54)!(3,4)(5,6);
s1 := Sym(54)!(1,5)(2,3)(4,6);
s2 := Sym(54)!( 8, 9)(10,11)(12,25)(13,28)(15,20)(16,19)(17,37)(18,40)(21,43)(22,44)(23,29)(24,26)(27,48)(30,47)(31,32)(33,49)(34,51)(35,38)(36,41)(39,53)(42,54)(45,46);
s3 := Sym(54)!( 7,10)( 8,19)( 9,15)(12,48)(13,47)(14,31)(16,20)(17,53)(18,54)(21,46)(22,45)(23,30)(24,27)(25,26)(28,29)(33,50)(34,52)(35,39)(36,42)(37,38)(40,41)(43,44);
s4 := Sym(54)!( 7,50)( 8,46)( 9,45)(10,53)(11,39)(12,40)(13,37)(14,52)(15,48)(16,30)(17,28)(18,25)(19,47)(20,27)(21,41)(22,38)(23,51)(24,49)(26,33)(29,34)(31,54)(32,42)(35,44)(36,43);
poly := sub<Sym(54)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 >;