Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,12,10}

Atlas Canonical Name {3,2,12,10}*1440

Overview

Group
SmallGroup(1440,5282)
Rank
5
Schläfli Type
{3,2,12,10}
Vertices, edges, …
3, 3, 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

5-fold

6-fold

10-fold

12-fold

15-fold

20-fold

30-fold

Covers minimal covers in bold

None in this atlas.

Representations

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