Part of the Atlas of Small Regular Polytopes

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

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

Overview

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