Polytope of Type {8,4,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,3}*768b
if this polytope has a name.
Group : SmallGroup(768,1086052)
Rank : 4
Schlafli Type : {8,4,3}
Number of vertices, edges, etc : 32, 64, 24, 3
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 8
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,3}*384a
   4-fold quotients : {4,4,3}*192a
   16-fold quotients : {2,4,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 7, 8)(11,12)(15,16)(17,24)(18,23)(19,21)(20,22)(25,31)(26,32)
(27,30)(28,29)(33,44)(34,43)(35,41)(36,42)(37,48)(38,47)(39,45)(40,46)(49,63)
(50,64)(51,62)(52,61)(53,60)(54,59)(55,57)(56,58);;
s1 := ( 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);;
s2 := ( 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);;
s3 := ( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,33)(18,34)(19,36)(20,35)
(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,46)(30,45)(31,47)
(32,48)(51,52)(53,58)(54,57)(55,59)(56,60)(61,62);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(64)!( 3, 4)( 7, 8)(11,12)(15,16)(17,24)(18,23)(19,21)(20,22)(25,31)
(26,32)(27,30)(28,29)(33,44)(34,43)(35,41)(36,42)(37,48)(38,47)(39,45)(40,46)
(49,63)(50,64)(51,62)(52,61)(53,60)(54,59)(55,57)(56,58);
s1 := 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);
s2 := 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);
s3 := Sym(64)!( 3, 4)( 5,10)( 6, 9)( 7,11)( 8,12)(13,14)(17,33)(18,34)(19,36)
(20,35)(21,42)(22,41)(23,43)(24,44)(25,38)(26,37)(27,39)(28,40)(29,46)(30,45)
(31,47)(32,48)(51,52)(53,58)(54,57)(55,59)(56,60)(61,62);
poly := sub<Sym(64)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 >;

References : None.
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