Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1920,236182)
Rank
6
Schläfli Type
{2,2,2,12,10}
Vertices, edges, …
2, 2, 2, 12, 60, 10
Order of s0s1s2s3s4s5
60
Order of s0s1s2s3s4s5s4s3s2s1
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 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (12,17)(13,18)(14,19)(15,20)(16,21)(27,32)(28,33)(29,34)(30,35)(31,36)(37,52)(38,53)(39,54)(40,55)(41,56)(42,62)(43,63)(44,64)(45,65)(46,66)(47,57)(48,58)(49,59)(50,60)(51,61);;
s4 := ( 7,42)( 8,46)( 9,45)(10,44)(11,43)(12,37)(13,41)(14,40)(15,39)(16,38)(17,47)(18,51)(19,50)(20,49)(21,48)(22,57)(23,61)(24,60)(25,59)(26,58)(27,52)(28,56)(29,55)(30,54)(31,53)(32,62)(33,66)(34,65)(35,64)(36,63);;
s5 := ( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,28)(29,31)(32,33)(34,36)(37,38)(39,41)(42,43)(44,46)(47,48)(49,51)(52,53)(54,56)(57,58)(59,61)(62,63)(64,66);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
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(66)!(1,2);
s1 := Sym(66)!(3,4);
s2 := Sym(66)!(5,6);
s3 := Sym(66)!(12,17)(13,18)(14,19)(15,20)(16,21)(27,32)(28,33)(29,34)(30,35)(31,36)(37,52)(38,53)(39,54)(40,55)(41,56)(42,62)(43,63)(44,64)(45,65)(46,66)(47,57)(48,58)(49,59)(50,60)(51,61);
s4 := Sym(66)!( 7,42)( 8,46)( 9,45)(10,44)(11,43)(12,37)(13,41)(14,40)(15,39)(16,38)(17,47)(18,51)(19,50)(20,49)(21,48)(22,57)(23,61)(24,60)(25,59)(26,58)(27,52)(28,56)(29,55)(30,54)(31,53)(32,62)(33,66)(34,65)(35,64)(36,63);
s5 := Sym(66)!( 7, 8)( 9,11)(12,13)(14,16)(17,18)(19,21)(22,23)(24,26)(27,28)(29,31)(32,33)(34,36)(37,38)(39,41)(42,43)(44,46)(47,48)(49,51)(52,53)(54,56)(57,58)(59,61)(62,63)(64,66);
poly := sub<Sym(66)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*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*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;