Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,2,12,6}

Atlas Canonical Name {4,2,12,6}*1152c

Overview

Group
SmallGroup(1152,136342)
Rank
5
Schläfli Type
{4,2,12,6}
Vertices, edges, …
4, 4, 12, 36, 6
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

9-fold

12-fold

18-fold

24-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 5,41)( 6,43)( 7,42)( 8,47)( 9,49)(10,48)(11,44)(12,46)(13,45)(14,50)(15,52)(16,51)(17,56)(18,58)(19,57)(20,53)(21,55)(22,54)(23,68)(24,70)(25,69)(26,74)(27,76)(28,75)(29,71)(30,73)(31,72)(32,59)(33,61)(34,60)(35,65)(36,67)(37,66)(38,62)(39,64)(40,63);;
s3 := ( 5,63)( 6,62)( 7,64)( 8,60)( 9,59)(10,61)(11,66)(12,65)(13,67)(14,72)(15,71)(16,73)(17,69)(18,68)(19,70)(20,75)(21,74)(22,76)(23,45)(24,44)(25,46)(26,42)(27,41)(28,43)(29,48)(30,47)(31,49)(32,54)(33,53)(34,55)(35,51)(36,50)(37,52)(38,57)(39,56)(40,58);;
s4 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,76);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*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(76)!(2,3);
s1 := Sym(76)!(1,2)(3,4);
s2 := Sym(76)!( 5,41)( 6,43)( 7,42)( 8,47)( 9,49)(10,48)(11,44)(12,46)(13,45)(14,50)(15,52)(16,51)(17,56)(18,58)(19,57)(20,53)(21,55)(22,54)(23,68)(24,70)(25,69)(26,74)(27,76)(28,75)(29,71)(30,73)(31,72)(32,59)(33,61)(34,60)(35,65)(36,67)(37,66)(38,62)(39,64)(40,63);
s3 := Sym(76)!( 5,63)( 6,62)( 7,64)( 8,60)( 9,59)(10,61)(11,66)(12,65)(13,67)(14,72)(15,71)(16,73)(17,69)(18,68)(19,70)(20,75)(21,74)(22,76)(23,45)(24,44)(25,46)(26,42)(27,41)(28,43)(29,48)(30,47)(31,49)(32,54)(33,53)(34,55)(35,51)(36,50)(37,52)(38,57)(39,56)(40,58);
s4 := Sym(76)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)(69,70)(72,73)(75,76);
poly := sub<Sym(76)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*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 >;