Part of the Atlas of Small Regular Polytopes

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

Atlas Canonical Name {2,2,2,2,56}*1792

Overview

Group
SmallGroup(1792,1083343)
Rank
6
Schläfli Type
{2,2,2,2,56}
Vertices, edges, …
2, 2, 2, 2, 56, 56
Order of s0s1s2s3s4s5
56
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 := (7,8);;
s4 := (10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,29)(24,28)(25,31)(26,30)(32,33)(35,42)(36,41)(37,44)(38,43)(39,46)(40,45)(47,48)(49,54)(50,53)(51,56)(52,55)(57,58)(59,62)(60,61)(63,64);;
s5 := ( 9,15)(10,12)(11,23)(13,25)(14,18)(16,20)(17,35)(19,37)(21,39)(22,28)(24,30)(26,32)(27,47)(29,49)(31,51)(33,40)(34,41)(36,43)(38,45)(42,57)(44,59)(46,52)(48,53)(50,55)(54,63)(56,60)(58,61)(62,64);;
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, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*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*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*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(64)!(1,2);
s1 := Sym(64)!(3,4);
s2 := Sym(64)!(5,6);
s3 := Sym(64)!(7,8);
s4 := Sym(64)!(10,11)(12,13)(14,17)(15,19)(16,18)(20,21)(22,27)(23,29)(24,28)(25,31)(26,30)(32,33)(35,42)(36,41)(37,44)(38,43)(39,46)(40,45)(47,48)(49,54)(50,53)(51,56)(52,55)(57,58)(59,62)(60,61)(63,64);
s5 := Sym(64)!( 9,15)(10,12)(11,23)(13,25)(14,18)(16,20)(17,35)(19,37)(21,39)(22,28)(24,30)(26,32)(27,47)(29,49)(31,51)(33,40)(34,41)(36,43)(38,45)(42,57)(44,59)(46,52)(48,53)(50,55)(54,63)(56,60)(58,61)(62,64);
poly := sub<Sym(64)|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, s3*s4*s3*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*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*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*s4*s5 >;