Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,157549)
Rank
5
Schläfli Type
{6,2,4,12}
Vertices, edges, …
6, 6, 4, 24, 12
Order of s0s1s2s3s4
12
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

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