Polytope of Type {2,44,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,44,4}*704
if this polytope has a name.
Group : SmallGroup(704,937)
Rank : 4
Schlafli Type : {2,44,4}
Number of vertices, edges, etc : 2, 44, 88, 4
Order of s₀s₁s₂s₃ : 44
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,44,4,2} of size 1408
Vertex Figure Of :
   {2,2,44,4} of size 1408
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,44,2}*352, {2,22,4}*352
   4-fold quotients : {2,22,2}*176
   8-fold quotients : {2,11,2}*88
   11-fold quotients : {2,4,4}*64
   22-fold quotients : {2,2,4}*32, {2,4,2}*32
   44-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,44,4}*1408, {2,44,8}*1408a, {2,88,4}*1408a, {2,44,8}*1408b, {2,88,4}*1408b, {2,44,4}*1408
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 >;

to this polytope