Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1792,1076200)
Rank
6
Schläfli Type
{2,2,2,28,4}
Vertices, edges, …
2, 2, 2, 28, 56, 4
Order of s0s1s2s3s4s5
28
Order of s0s1s2s3s4s5s4s3s2s1
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

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8,13)( 9,12)(10,11)(15,20)(16,19)(17,18)(22,27)(23,26)(24,25)(29,34)(30,33)(31,32)(35,49)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,56)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57);;
s4 := ( 7,36)( 8,35)( 9,41)(10,40)(11,39)(12,38)(13,37)(14,43)(15,42)(16,48)(17,47)(18,46)(19,45)(20,44)(21,50)(22,49)(23,55)(24,54)(25,53)(26,52)(27,51)(28,57)(29,56)(30,62)(31,61)(32,60)(33,59)(34,58);;
s5 := (35,42)(36,43)(37,44)(38,45)(39,46)(40,47)(41,48)(49,56)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, 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(62)!(1,2);
s1 := Sym(62)!(3,4);
s2 := Sym(62)!(5,6);
s3 := Sym(62)!( 8,13)( 9,12)(10,11)(15,20)(16,19)(17,18)(22,27)(23,26)(24,25)(29,34)(30,33)(31,32)(35,49)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,56)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57);
s4 := Sym(62)!( 7,36)( 8,35)( 9,41)(10,40)(11,39)(12,38)(13,37)(14,43)(15,42)(16,48)(17,47)(18,46)(19,45)(20,44)(21,50)(22,49)(23,55)(24,54)(25,53)(26,52)(27,51)(28,57)(29,56)(30,62)(31,61)(32,60)(33,59)(34,58);
s5 := Sym(62)!(35,42)(36,43)(37,44)(38,45)(39,46)(40,47)(41,48)(49,56)(50,57)(51,58)(52,59)(53,60)(54,61)(55,62);
poly := sub<Sym(62)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s5*s4*s3*s4*s5*s4, 
s4*s5*s4*s5*s4*s5*s4*s5, 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 >;