Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,2,22,8}

Atlas Canonical Name {2,2,22,8}*1408

Overview

Group
SmallGroup(1408,19224)
Rank
5
Schläfli Type
{2,2,22,8}
Vertices, edges, …
2, 2, 22, 88, 8
Order of s0s1s2s3s4
88
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

8-fold

11-fold

22-fold

44-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP)
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(17,26)(18,25)(19,24)(20,23)(21,22)(28,37)(29,36)(30,35)(31,34)(32,33)(39,48)(40,47)(41,46)(42,45)(43,44)(50,59)(51,58)(52,57)(53,56)(54,55)(61,70)(62,69)(63,68)(64,67)(65,66)(72,81)(73,80)(74,79)(75,78)(76,77)(83,92)(84,91)(85,90)(86,89)(87,88);;
s3 := ( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,17)(18,26)(19,25)(20,24)(21,23)(27,39)(28,38)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(49,72)(50,71)(51,81)(52,80)(53,79)(54,78)(55,77)(56,76)(57,75)(58,74)(59,73)(60,83)(61,82)(62,92)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)(70,84);;
s4 := ( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)(22,66)(23,67)(24,68)(25,69)(26,70)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)(47,80)(48,81);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*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(92)!(1,2);
s1 := Sym(92)!(3,4);
s2 := Sym(92)!( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(17,26)(18,25)(19,24)(20,23)(21,22)(28,37)(29,36)(30,35)(31,34)(32,33)(39,48)(40,47)(41,46)(42,45)(43,44)(50,59)(51,58)(52,57)(53,56)(54,55)(61,70)(62,69)(63,68)(64,67)(65,66)(72,81)(73,80)(74,79)(75,78)(76,77)(83,92)(84,91)(85,90)(86,89)(87,88);
s3 := Sym(92)!( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,17)(18,26)(19,25)(20,24)(21,23)(27,39)(28,38)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(49,72)(50,71)(51,81)(52,80)(53,79)(54,78)(55,77)(56,76)(57,75)(58,74)(59,73)(60,83)(61,82)(62,92)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)(70,84);
s4 := Sym(92)!( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)(22,66)(23,67)(24,68)(25,69)(26,70)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)(37,92)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)(47,80)(48,81);
poly := sub<Sym(92)|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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*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 >;