Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,2,4,22}

Atlas Canonical Name {3,2,4,22}*1056

Overview

Group
SmallGroup(1056,926)
Rank
5
Schläfli Type
{3,2,4,22}
Vertices, edges, …
3, 3, 4, 44, 22
Order of s0s1s2s3s4
132
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

11-fold

22-fold

Covers minimal covers in bold

None in this atlas.

Representations

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