Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,2,12,3}

Atlas Canonical Name {6,2,12,3}*1152

Overview

Group
SmallGroup(1152,157603)
Rank
5
Schläfli Type
{6,2,12,3}
Vertices, edges, …
6, 6, 16, 24, 4
Order of s0s1s2s3s4
24
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

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 := ( 7,15)( 8,10)( 9,31)(11,16)(12,54)(13,53)(14,19)(17,48)(18,47)(20,32)(21,52)(22,50)(23,42)(24,39)(25,38)(26,40)(27,36)(28,41)(29,37)(30,35)(33,46)(34,45)(43,49)(44,51);;
s4 := ( 7,52)( 8,46)( 9,45)(10,42)(11,54)(12,17)(13,18)(14,50)(15,30)(16,48)(19,27)(20,47)(21,35)(22,36)(23,33)(24,34)(25,37)(26,51)(28,40)(29,49)(31,39)(32,53)(38,43)(41,44);;
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, 
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*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)!( 7,15)( 8,10)( 9,31)(11,16)(12,54)(13,53)(14,19)(17,48)(18,47)(20,32)(21,52)(22,50)(23,42)(24,39)(25,38)(26,40)(27,36)(28,41)(29,37)(30,35)(33,46)(34,45)(43,49)(44,51);
s4 := Sym(54)!( 7,52)( 8,46)( 9,45)(10,42)(11,54)(12,17)(13,18)(14,50)(15,30)(16,48)(19,27)(20,47)(21,35)(22,36)(23,33)(24,34)(25,37)(26,51)(28,40)(29,49)(31,39)(32,53)(38,43)(41,44);
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, s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s4*s2*s3 >;