Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,2,30,4}

Atlas Canonical Name {4,2,30,4}*1920a

Overview

Group
SmallGroup(1920,208100)
Rank
5
Schläfli Type
{4,2,30,4}
Vertices, edges, …
4, 4, 30, 60, 4
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

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