Polytope of Type {8,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,12}*768i
if this polytope has a name.
Group : SmallGroup(768,1086052)
Rank : 3
Schlafli Type : {8,12}
Number of vertices, edges, etc : 32, 192, 48
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 : {8,6}*384b
   4-fold quotients : {4,6}*192a
   16-fold quotients : {4,6}*48c
   32-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {8,12}

Twisty Puzzle