Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,28}

Atlas Canonical Name {3,2,4,28}*1344

Overview

Group
SmallGroup(1344,7765)
Rank
5
Schläfli Type
{3,2,4,28}
Vertices, edges, …
3, 3, 4, 56, 28
Order of s0s1s2s3s4
84
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

None in this atlas.

Representations

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