Polytope of Type {4,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,9}*1152
if this polytope has a name.
Group : SmallGroup(1152,157853)
Rank : 3
Schlafli Type : {4,9}
Number of vertices, edges, etc : 64, 288, 144
Order of s₀s₁s₂ : 9
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,33)( 2,34)( 3,35)( 4,36)( 5,37)( 6,38)( 7,39)( 8,40)( 9,41)(10,42)
(11,43)(12,44)(13,45)(14,46)(15,47)(16,48)(17,49)(18,50)(19,51)(20,52)(21,53)
(22,54)(23,55)(24,56)(25,57)(26,58)(27,59)(28,60)(29,61)(30,62)(31,63)
(32,64);;
s1 := ( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)(13,33)
(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)(31,40)
(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60);;
s2 := ( 2, 9)( 3,13)( 4, 5)( 6,12)( 7,16)(11,14)(17,49)(18,57)(19,61)(20,53)
(21,52)(22,60)(23,64)(24,56)(25,50)(26,58)(27,62)(28,54)(29,51)(30,59)(31,63)
(32,55)(34,41)(35,45)(36,37)(38,44)(39,48)(43,46);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(64)!( 1,33)( 2,34)( 3,35)( 4,36)( 5,37)( 6,38)( 7,39)( 8,40)( 9,41)
(10,42)(11,43)(12,44)(13,45)(14,46)(15,47)(16,48)(17,49)(18,50)(19,51)(20,52)
(21,53)(22,54)(23,55)(24,56)(25,57)(26,58)(27,59)(28,60)(29,61)(30,62)(31,63)
(32,64);
s1 := Sym(64)!( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)
(13,33)(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)
(31,40)(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60);
s2 := Sym(64)!( 2, 9)( 3,13)( 4, 5)( 6,12)( 7,16)(11,14)(17,49)(18,57)(19,61)
(20,53)(21,52)(22,60)(23,64)(24,56)(25,50)(26,58)(27,62)(28,54)(29,51)(30,59)
(31,63)(32,55)(34,41)(35,45)(36,37)(38,44)(39,48)(43,46);
poly := sub<Sym(64)|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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >;

References : None.
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