Part of the Atlas of Small Regular Polytopes

Polytope of Type {60,2,8}

Atlas Canonical Name {60,2,8}*1920

Overview

Group
SmallGroup(1920,182091)
Rank
4
Schläfli Type
{60,2,8}
Vertices, edges, …
60, 60, 8, 8
Order of s0s1s2s3
120
Order of s0s1s2s3s2s1
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

8-fold

10-fold

12-fold

15-fold

16-fold

20-fold

24-fold

30-fold

40-fold

48-fold

60-fold

80-fold

120-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 2, 3)( 4, 5)( 6, 7)( 9,14)(10,13)(11,16)(12,15)(17,20)(18,19)(21,22)(23,24)(25,26)(27,36)(28,35)(29,34)(30,33)(31,38)(32,37)(39,42)(40,41)(43,46)(44,45)(47,48)(49,56)(50,55)(51,54)(52,53)(57,60)(58,59);;
s1 := ( 1,27)( 2,17)( 3,43)( 4,11)( 5,29)( 6, 9)( 7,49)( 8,33)(10,19)(12,39)(13,25)(14,45)(15,23)(16,57)(18,31)(20,51)(21,28)(22,50)(24,35)(26,53)(30,41)(32,40)(34,47)(36,59)(37,44)(38,58)(42,52)(46,55)(48,54)(56,60);;
s2 := (62,63)(64,65)(66,67);;
s3 := (61,62)(63,64)(65,66)(67,68);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(68)!( 2, 3)( 4, 5)( 6, 7)( 9,14)(10,13)(11,16)(12,15)(17,20)(18,19)(21,22)(23,24)(25,26)(27,36)(28,35)(29,34)(30,33)(31,38)(32,37)(39,42)(40,41)(43,46)(44,45)(47,48)(49,56)(50,55)(51,54)(52,53)(57,60)(58,59);
s1 := Sym(68)!( 1,27)( 2,17)( 3,43)( 4,11)( 5,29)( 6, 9)( 7,49)( 8,33)(10,19)(12,39)(13,25)(14,45)(15,23)(16,57)(18,31)(20,51)(21,28)(22,50)(24,35)(26,53)(30,41)(32,40)(34,47)(36,59)(37,44)(38,58)(42,52)(46,55)(48,54)(56,60);
s2 := Sym(68)!(62,63)(64,65)(66,67);
s3 := Sym(68)!(61,62)(63,64)(65,66)(67,68);
poly := sub<Sym(68)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;