Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1792,1076200)
Rank
6
Schläfli Type
{2,2,2,4,28}
Vertices, edges, …
2, 2, 2, 4, 56, 28
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 := (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);;
s4 := ( 7,35)( 8,41)( 9,40)(10,39)(11,38)(12,37)(13,36)(14,42)(15,48)(16,47)(17,46)(18,45)(19,44)(20,43)(21,49)(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)(28,56)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57);;
s5 := ( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,22)(23,27)(24,26)(28,29)(30,34)(31,33)(35,50)(36,49)(37,55)(38,54)(39,53)(40,52)(41,51)(42,57)(43,56)(44,62)(45,61)(46,60)(47,59)(48,58);;
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*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(62)!(1,2);
s1 := Sym(62)!(3,4);
s2 := Sym(62)!(5,6);
s3 := 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);
s4 := Sym(62)!( 7,35)( 8,41)( 9,40)(10,39)(11,38)(12,37)(13,36)(14,42)(15,48)(16,47)(17,46)(18,45)(19,44)(20,43)(21,49)(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)(28,56)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57);
s5 := Sym(62)!( 7, 8)( 9,13)(10,12)(14,15)(16,20)(17,19)(21,22)(23,27)(24,26)(28,29)(30,34)(31,33)(35,50)(36,49)(37,55)(38,54)(39,53)(40,52)(41,51)(42,57)(43,56)(44,62)(45,61)(46,60)(47,59)(48,58);
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*s3*s4*s3*s4*s3*s4, 
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;