Part of the Atlas of Small Regular Polytopes

Polytope of Type {56,2,2,4}

Atlas Canonical Name {56,2,2,4}*1792

Overview

Group
SmallGroup(1792,1044763)
Rank
5
Schläfli Type
{56,2,2,4}
Vertices, edges, …
56, 56, 2, 4, 4
Order of s0s1s2s3s4
56
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

16-fold

28-fold

56-fold

Covers minimal covers in bold

None in this atlas.

Representations

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