Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,2,10,12}

Atlas Canonical Name {4,2,10,12}*1920

Overview

Group
SmallGroup(1920,208125)
Rank
5
Schläfli Type
{4,2,10,12}
Vertices, edges, …
4, 4, 10, 60, 12
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

4-fold

5-fold

6-fold

10-fold

12-fold

15-fold

20-fold

24-fold

30-fold

40-fold

60-fold

Covers minimal covers in bold

None in this atlas.

Representations

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