Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*768a
if this polytope has a name.
Group : SmallGroup(768,1086051)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 64, 192, 48
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {4,6}*192a
   16-fold quotients : {4,6}*48c
   32-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope