Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,12,6}

Atlas Canonical Name {2,12,6}*288c

Overview

Group
SmallGroup(288,977)
Rank
4
Schläfli Type
{2,12,6}
Vertices, edges, …
2, 12, 36, 6
Order of s0s1s2s3
12
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

9-fold

12-fold

18-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(21,30)(22,32)(23,31)(24,33)(25,35)(26,34)(27,36)(28,38)(29,37)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73);;
s2 := ( 3,58)( 4,57)( 5,59)( 6,64)( 7,63)( 8,65)( 9,61)(10,60)(11,62)(12,67)(13,66)(14,68)(15,73)(16,72)(17,74)(18,70)(19,69)(20,71)(21,40)(22,39)(23,41)(24,46)(25,45)(26,47)(27,43)(28,42)(29,44)(30,49)(31,48)(32,50)(33,55)(34,54)(35,56)(36,52)(37,51)(38,53);;
s3 := ( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)(23,61)(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)(34,68)(35,67)(36,72)(37,74)(38,73);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(21,30)(22,32)(23,31)(24,33)(25,35)(26,34)(27,36)(28,38)(29,37)(40,41)(43,44)(46,47)(49,50)(52,53)(55,56)(57,66)(58,68)(59,67)(60,69)(61,71)(62,70)(63,72)(64,74)(65,73);
s2 := Sym(74)!( 3,58)( 4,57)( 5,59)( 6,64)( 7,63)( 8,65)( 9,61)(10,60)(11,62)(12,67)(13,66)(14,68)(15,73)(16,72)(17,74)(18,70)(19,69)(20,71)(21,40)(22,39)(23,41)(24,46)(25,45)(26,47)(27,43)(28,42)(29,44)(30,49)(31,48)(32,50)(33,55)(34,54)(35,56)(36,52)(37,51)(38,53);
s3 := Sym(74)!( 3,42)( 4,44)( 5,43)( 6,39)( 7,41)( 8,40)( 9,45)(10,47)(11,46)(12,51)(13,53)(14,52)(15,48)(16,50)(17,49)(18,54)(19,56)(20,55)(21,60)(22,62)(23,61)(24,57)(25,59)(26,58)(27,63)(28,65)(29,64)(30,69)(31,71)(32,70)(33,66)(34,68)(35,67)(36,72)(37,74)(38,73);
poly := sub<Sym(74)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;