Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*768b
if this polytope has a name.
Group : SmallGroup(768,1086052)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 64, 192, 48
Order of s₀s₁s₂ : 12
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) :
   2-fold quotients : {8,6}*384b
   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)( 9,60)(10,59)
(11,58)(12,57)(13,62)(14,61)(15,64)(16,63)(17,33)(18,34)(19,35)(20,36)(21,39)
(22,40)(23,37)(24,38)(25,44)(26,43)(27,42)(28,41)(29,46)(30,45)(31,48)
(32,47);;
s1 := ( 5, 6)( 7, 8)( 9,13)(10,14)(11,15)(12,16)(17,24)(18,23)(19,22)(20,21)
(25,28)(26,27)(29,31)(30,32)(33,63)(34,64)(35,61)(36,62)(37,59)(38,60)(39,57)
(40,58)(41,52)(42,51)(43,50)(44,49)(45,55)(46,56)(47,53)(48,54);;
s2 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,33)(18,34)(19,36)(20,35)
(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,46)(30,45)(31,47)
(32,48)(51,52)(53,58)(54,57)(55,59)(56,60)(61,62);;
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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*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)( 9,60)
(10,59)(11,58)(12,57)(13,62)(14,61)(15,64)(16,63)(17,33)(18,34)(19,35)(20,36)
(21,39)(22,40)(23,37)(24,38)(25,44)(26,43)(27,42)(28,41)(29,46)(30,45)(31,48)
(32,47);
s1 := Sym(64)!( 5, 6)( 7, 8)( 9,13)(10,14)(11,15)(12,16)(17,24)(18,23)(19,22)
(20,21)(25,28)(26,27)(29,31)(30,32)(33,63)(34,64)(35,61)(36,62)(37,59)(38,60)
(39,57)(40,58)(41,52)(42,51)(43,50)(44,49)(45,55)(46,56)(47,53)(48,54);
s2 := Sym(64)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,33)(18,34)(19,36)
(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,46)(30,45)
(31,47)(32,48)(51,52)(53,58)(54,57)(55,59)(56,60)(61,62);
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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope