Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,3,2,56}

Atlas Canonical Name {2,3,2,56}*1344

Overview

Group
SmallGroup(1344,8483)
Rank
5
Schläfli Type
{2,3,2,56}
Vertices, edges, …
2, 3, 3, 56, 56
Order of s0s1s2s3s4
168
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 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := ( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,18)(19,24)(20,26)(21,25)(22,28)(23,27)(29,30)(32,39)(33,38)(34,41)(35,40)(36,43)(37,42)(44,45)(46,51)(47,50)(48,53)(49,52)(54,55)(56,59)(57,58)(60,61);;
s4 := ( 6,12)( 7, 9)( 8,20)(10,22)(11,15)(13,17)(14,32)(16,34)(18,36)(19,25)(21,27)(23,29)(24,44)(26,46)(28,48)(30,37)(31,38)(33,40)(35,42)(39,54)(41,56)(43,49)(45,50)(47,52)(51,60)(53,57)(55,58)(59,61);;
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, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 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*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(61)!(1,2);
s1 := Sym(61)!(4,5);
s2 := Sym(61)!(3,4);
s3 := Sym(61)!( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,18)(19,24)(20,26)(21,25)(22,28)(23,27)(29,30)(32,39)(33,38)(34,41)(35,40)(36,43)(37,42)(44,45)(46,51)(47,50)(48,53)(49,52)(54,55)(56,59)(57,58)(60,61);
s4 := Sym(61)!( 6,12)( 7, 9)( 8,20)(10,22)(11,15)(13,17)(14,32)(16,34)(18,36)(19,25)(21,27)(23,29)(24,44)(26,46)(28,48)(30,37)(31,38)(33,40)(35,42)(39,54)(41,56)(43,49)(45,50)(47,52)(51,60)(53,57)(55,58)(59,61);
poly := sub<Sym(61)|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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2, 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*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 >;