Polytope of Type {6,8}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope