Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1152,134264)
Rank
5
Schläfli Type
{2,6,12,4}
Vertices, edges, …
2, 6, 36, 24, 4
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

9-fold

12-fold

18-fold

24-fold

36-fold

Covers minimal covers in bold

None in this atlas.

Representations

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