Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*768b
if this polytope has a name.
Group : SmallGroup(768,1086052)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 64, 192, 32
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 6
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 := ( 1,38)( 2,37)( 3,40)( 4,39)( 5,43)( 6,44)( 7,41)( 8,42)( 9,46)(10,45)
(11,48)(12,47)(13,36)(14,35)(15,34)(16,33)(17,25)(18,26)(19,27)(20,28)(21,23)
(22,24)(29,32)(30,31)(53,64)(54,63)(55,62)(56,61)(57,58)(59,60);;
s2 := ( 1,18)( 2,17)( 3,19)( 4,20)( 5,22)( 6,21)( 7,23)( 8,24)( 9,31)(10,32)
(11,30)(12,29)(13,28)(14,27)(15,25)(16,26)(33,34)(37,38)(41,47)(42,48)(43,46)
(44,45)(49,50)(53,54)(57,63)(58,64)(59,62)(60,61);;
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, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s2*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)!( 1,38)( 2,37)( 3,40)( 4,39)( 5,43)( 6,44)( 7,41)( 8,42)( 9,46)
(10,45)(11,48)(12,47)(13,36)(14,35)(15,34)(16,33)(17,25)(18,26)(19,27)(20,28)
(21,23)(22,24)(29,32)(30,31)(53,64)(54,63)(55,62)(56,61)(57,58)(59,60);
s2 := Sym(64)!( 1,18)( 2,17)( 3,19)( 4,20)( 5,22)( 6,21)( 7,23)( 8,24)( 9,31)
(10,32)(11,30)(12,29)(13,28)(14,27)(15,25)(16,26)(33,34)(37,38)(41,47)(42,48)
(43,46)(44,45)(49,50)(53,54)(57,63)(58,64)(59,62)(60,61);
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, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s2*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