Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,12,10,2}

Atlas Canonical Name {2,12,10,2}*960

Overview

Group
SmallGroup(960,11208)
Rank
5
Schläfli Type
{2,12,10,2}
Vertices, edges, …
2, 12, 60, 10, 2
Order of s0s1s2s3s4
60
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

5-fold

6-fold

10-fold

12-fold

15-fold

20-fold

30-fold

Covers minimal covers in bold

2-fold

Representations

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