Polytope of Type {44,4,2}

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

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

Permutation Representation (Magma) :

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

to this polytope