Polytope of Type {16,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,6}*768a
Also Known As : {16,6}₃. if this polytope has another name.
Group : SmallGroup(768,1085833)
Rank : 3
Schlafli Type : {16,6}
Number of vertices, edges, etc : 64, 192, 24
Order of s₀s₁s₂ : 3
Order of s₀s₁s₂s₁ : 16
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 : {8,6}*192a
   16-fold quotients : {4,6}*48b
   32-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope