Polytope of Type {2,4,44}

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

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

to this polytope