Polytope of Type {22,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,8}*352
Also Known As : {22,8|2}. if this polytope has another name.
Group : SmallGroup(352,105)
Rank : 3
Schlafli Type : {22,8}
Number of vertices, edges, etc : 22, 88, 8
Order of s₀s₁s₂ : 88
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {22,8,2} of size 704
   {22,8,4} of size 1408
   {22,8,4} of size 1408
Vertex Figure Of :
   {2,22,8} of size 704
   {4,22,8} of size 1408
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {22,4}*176
   4-fold quotients : {22,2}*88
   8-fold quotients : {11,2}*44
   11-fold quotients : {2,8}*32
   22-fold quotients : {2,4}*16
   44-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {44,8}*704a, {22,16}*704
   3-fold covers : {22,24}*1056, {66,8}*1056
   4-fold covers : {44,8}*1408a, {88,8}*1408a, {88,8}*1408c, {44,16}*1408a, {44,16}*1408b, {22,32}*1408
   5-fold covers : {22,40}*1760, {110,8}*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)(46,55)
(47,54)(48,53)(49,52)(50,51)(57,66)(58,65)(59,64)(60,63)(61,62)(68,77)(69,76)
(70,75)(71,74)(72,73)(79,88)(80,87)(81,86)(82,85)(83,84);;
s1 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)(17,19)
(23,35)(24,34)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)
(45,68)(46,67)(47,77)(48,76)(49,75)(50,74)(51,73)(52,72)(53,71)(54,70)(55,69)
(56,79)(57,78)(58,88)(59,87)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81)
(66,80);;
s2 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)
(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)
(22,66)(23,78)(24,79)(25,80)(26,81)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)
(33,88)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)
(44,77);;
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*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 ];;
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)
(46,55)(47,54)(48,53)(49,52)(50,51)(57,66)(58,65)(59,64)(60,63)(61,62)(68,77)
(69,76)(70,75)(71,74)(72,73)(79,88)(80,87)(81,86)(82,85)(83,84);
s1 := Sym(88)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)
(17,19)(23,35)(24,34)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)
(33,36)(45,68)(46,67)(47,77)(48,76)(49,75)(50,74)(51,73)(52,72)(53,71)(54,70)
(55,69)(56,79)(57,78)(58,88)(59,87)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81)
(66,80);
s2 := Sym(88)!( 1,45)( 2,46)( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)
(10,54)(11,55)(12,56)(13,57)(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)
(21,65)(22,66)(23,78)(24,79)(25,80)(26,81)(27,82)(28,83)(29,84)(30,85)(31,86)
(32,87)(33,88)(34,67)(35,68)(36,69)(37,70)(38,71)(39,72)(40,73)(41,74)(42,75)
(43,76)(44,77);
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*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 >;

References : None.
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