Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,44,4}

Atlas Canonical Name {2,44,4}*704

Overview

Group
SmallGroup(704,937)
Rank
4
Schläfli Type
{2,44,4}
Vertices, edges, …
2, 44, 88, 4
Order of s0s1s2s3
44
Order of s0s1s2s3s2s1
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

2-fold

Representations

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