Part of the Atlas of Small Regular Polytopes

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

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

Overview

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