Polytope of Type {44,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,4}*352
Also Known As : {44,4|2}. if this polytope has another name.
Group : SmallGroup(352,77)
Rank : 3
Schlafli Type : {44,4}
Number of vertices, edges, etc : 44, 88, 4
Order of s₀s₁s₂ : 44
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {44,4,2} of size 704
   {44,4,4} of size 1408
Vertex Figure Of :
   {2,44,4} of size 704
   {4,44,4} of size 1408
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {44,2}*176, {22,4}*176
   4-fold quotients : {22,2}*88
   8-fold quotients : {11,2}*44
   11-fold quotients : {4,4}*32
   22-fold quotients : {2,4}*16, {4,2}*16
   44-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {88,4}*704a, {44,4}*704, {88,4}*704b, {44,8}*704a, {44,8}*704b
   3-fold covers : {44,12}*1056, {132,4}*1056a
   4-fold covers : {44,8}*1408a, {88,4}*1408a, {88,8}*1408a, {88,8}*1408b, {88,8}*1408c, {88,8}*1408d, {44,16}*1408a, {176,4}*1408a, {44,16}*1408b, {176,4}*1408b, {44,4}*1408, {88,4}*1408b, {44,8}*1408b
   5-fold covers : {44,20}*1760, {220,4}*1760
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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(88)!( 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(88)!( 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(88)!(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);
poly := sub<Sym(88)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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 >;

References : None.
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