Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,2,28,4}

Atlas Canonical Name {4,2,28,4}*1792

Overview

Group
SmallGroup(1792,364865)
Rank
5
Schläfli Type
{4,2,28,4}
Vertices, edges, …
4, 4, 28, 56, 4
Order of s0s1s2s3s4
28
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

4-fold

7-fold

8-fold

14-fold

16-fold

28-fold

56-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)(28,31)(29,30)(33,47)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,54)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55);;
s3 := ( 5,34)( 6,33)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,41)(13,40)(14,46)(15,45)(16,44)(17,43)(18,42)(19,48)(20,47)(21,53)(22,52)(23,51)(24,50)(25,49)(26,55)(27,54)(28,60)(29,59)(30,58)(31,57)(32,56);;
s4 := (33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(47,54)(48,55)(49,56)(50,57)(51,58)(52,59)(53,60);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(60)!(2,3);
s1 := Sym(60)!(1,2)(3,4);
s2 := Sym(60)!( 6,11)( 7,10)( 8, 9)(13,18)(14,17)(15,16)(20,25)(21,24)(22,23)(27,32)(28,31)(29,30)(33,47)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,54)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55);
s3 := Sym(60)!( 5,34)( 6,33)( 7,39)( 8,38)( 9,37)(10,36)(11,35)(12,41)(13,40)(14,46)(15,45)(16,44)(17,43)(18,42)(19,48)(20,47)(21,53)(22,52)(23,51)(24,50)(25,49)(26,55)(27,54)(28,60)(29,59)(30,58)(31,57)(32,56);
s4 := Sym(60)!(33,40)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(47,54)(48,55)(49,56)(50,57)(51,58)(52,59)(53,60);
poly := sub<Sym(60)|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 >;