Polytope of Type {6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*768a
if this polytope has a name.
Group : SmallGroup(768,1086052)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 32, 192, 64
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 3
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {6,6}*384a
   4-fold quotients : {6,6}*192a
   32-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope