Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1920,208125)
Rank
5
Schläfli Type
{10,12,2,4}
Vertices, edges, …
10, 60, 12, 4, 4
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, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59);;
s1 := ( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)(21,27)(22,26)(23,30)(24,29)(25,28)(31,47)(32,46)(33,50)(34,49)(35,48)(36,57)(37,56)(38,60)(39,59)(40,58)(41,52)(42,51)(43,55)(44,54)(45,53);;
s2 := ( 1,36)( 2,37)( 3,38)( 4,39)( 5,40)( 6,31)( 7,32)( 8,33)( 9,34)(10,35)(11,41)(12,42)(13,43)(14,44)(15,45)(16,51)(17,52)(18,53)(19,54)(20,55)(21,46)(22,47)(23,48)(24,49)(25,50)(26,56)(27,57)(28,58)(29,59)(30,60);;
s3 := (62,63);;
s4 := (61,62)(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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59);
s1 := Sym(64)!( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)(21,27)(22,26)(23,30)(24,29)(25,28)(31,47)(32,46)(33,50)(34,49)(35,48)(36,57)(37,56)(38,60)(39,59)(40,58)(41,52)(42,51)(43,55)(44,54)(45,53);
s2 := Sym(64)!( 1,36)( 2,37)( 3,38)( 4,39)( 5,40)( 6,31)( 7,32)( 8,33)( 9,34)(10,35)(11,41)(12,42)(13,43)(14,44)(15,45)(16,51)(17,52)(18,53)(19,54)(20,55)(21,46)(22,47)(23,48)(24,49)(25,50)(26,56)(27,57)(28,58)(29,59)(30,60);
s3 := Sym(64)!(62,63);
s4 := Sym(64)!(61,62)(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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;