Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1920,208100)
Rank
5
Schläfli Type
{4,2,4,30}
Vertices, edges, …
4, 4, 4, 60, 30
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 := (35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)(46,61)(47,62)(48,63)(49,64);;
s3 := ( 5,35)( 6,39)( 7,38)( 8,37)( 9,36)(10,45)(11,49)(12,48)(13,47)(14,46)(15,40)(16,44)(17,43)(18,42)(19,41)(20,50)(21,54)(22,53)(23,52)(24,51)(25,60)(26,64)(27,63)(28,62)(29,61)(30,55)(31,59)(32,58)(33,57)(34,56);;
s4 := ( 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)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)(47,49)(50,56)(51,55)(52,59)(53,58)(54,57)(60,61)(62,64);;
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*s2*s3*s2*s3*s2*s3, 
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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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(64)!(2,3);
s1 := Sym(64)!(1,2)(3,4);
s2 := Sym(64)!(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)(46,61)(47,62)(48,63)(49,64);
s3 := Sym(64)!( 5,35)( 6,39)( 7,38)( 8,37)( 9,36)(10,45)(11,49)(12,48)(13,47)(14,46)(15,40)(16,44)(17,43)(18,42)(19,41)(20,50)(21,54)(22,53)(23,52)(24,51)(25,60)(26,64)(27,63)(28,62)(29,61)(30,55)(31,59)(32,58)(33,57)(34,56);
s4 := 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)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)(47,49)(50,56)(51,55)(52,59)(53,58)(54,57)(60,61)(62,64);
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*s2*s3*s2*s3*s2*s3, 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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;