Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,4,28}*896

Overview

Group
SmallGroup(896,17525)
Rank
5
Schläfli Type
{2,2,4,28}
Vertices, edges, …
2, 2, 4, 56, 28
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

28-fold

Covers minimal covers in bold

2-fold

Representations

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