Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*768j
if this polytope has a name.
Group : SmallGroup(768,1086052)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 48, 192, 32
Order of s₀s₁s₂ : 6
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 : {6,8}*384b
   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)( 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 := ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,30)(10,29)
(11,32)(12,31)(13,26)(14,25)(15,28)(16,27)(33,56)(34,55)(35,54)(36,53)(37,52)
(38,51)(39,50)(40,49)(41,62)(42,61)(43,64)(44,63)(45,58)(46,57)(47,60)
(48,59);;
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*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 ];;
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)!( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,30)
(10,29)(11,32)(12,31)(13,26)(14,25)(15,28)(16,27)(33,56)(34,55)(35,54)(36,53)
(37,52)(38,51)(39,50)(40,49)(41,62)(42,61)(43,64)(44,63)(45,58)(46,57)(47,60)
(48,59);
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*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0 >;

References : None.
to this polytope