Part of the Atlas of Small Regular Polytopes

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

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

Overview

Group
SmallGroup(1056,926)
Rank
5
Schläfli Type
{3,2,22,4}
Vertices, edges, …
3, 3, 22, 44, 4
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 := ( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(16,25)(17,24)(18,23)(19,22)(20,21)(27,36)(28,35)(29,34)(30,33)(31,32)(38,47)(39,46)(40,45)(41,44)(42,43);;
s3 := ( 4, 5)( 6,14)( 7,13)( 8,12)( 9,11)(15,16)(17,25)(18,24)(19,23)(20,22)(26,38)(27,37)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39);;
s4 := ( 4,26)( 5,27)( 6,28)( 7,29)( 8,30)( 9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,47);;
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(47)!(2,3);
s1 := Sym(47)!(1,2);
s2 := Sym(47)!( 5,14)( 6,13)( 7,12)( 8,11)( 9,10)(16,25)(17,24)(18,23)(19,22)(20,21)(27,36)(28,35)(29,34)(30,33)(31,32)(38,47)(39,46)(40,45)(41,44)(42,43);
s3 := Sym(47)!( 4, 5)( 6,14)( 7,13)( 8,12)( 9,11)(15,16)(17,25)(18,24)(19,23)(20,22)(26,38)(27,37)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39);
s4 := Sym(47)!( 4,26)( 5,27)( 6,28)( 7,29)( 8,30)( 9,31)(10,32)(11,33)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,47);
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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;