Polytope of Type {4,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,4}*768f
if this polytope has a name.
Group : SmallGroup(768,1090070)
Rank : 4
Schlafli Type : {4,6,4}
Number of vertices, edges, etc : 4, 48, 48, 16
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
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) :
   4-fold quotients : {4,6,4}*192d
   8-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)
(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,33)(18,34)(19,35)(20,36)(21,37)
(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)(28,44)(29,45)(30,46)(31,47)
(32,48);;
s1 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)
(27,32)(28,31)(33,49)(34,50)(35,52)(36,51)(37,53)(38,54)(39,56)(40,55)(41,61)
(42,62)(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);;
s2 := ( 2, 3)( 5,11)( 6, 9)( 7,12)( 8,10)(13,16)(17,33)(18,35)(19,34)(20,36)
(21,43)(22,41)(23,44)(24,42)(25,38)(26,40)(27,37)(28,39)(29,48)(30,46)(31,47)
(32,45)(50,51)(53,59)(54,57)(55,60)(56,58)(61,64);;
s3 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,13)(10,14)(11,15)(12,16)(17,21)(18,22)
(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)(41,45)
(42,46)(43,47)(44,48)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)
(60,64);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(64)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)
(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,33)(18,34)(19,35)(20,36)
(21,37)(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)(28,44)(29,45)(30,46)(31,47)
(32,48);
s1 := Sym(64)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)
(26,30)(27,32)(28,31)(33,49)(34,50)(35,52)(36,51)(37,53)(38,54)(39,56)(40,55)
(41,61)(42,62)(43,64)(44,63)(45,57)(46,58)(47,60)(48,59);
s2 := Sym(64)!( 2, 3)( 5,11)( 6, 9)( 7,12)( 8,10)(13,16)(17,33)(18,35)(19,34)
(20,36)(21,43)(22,41)(23,44)(24,42)(25,38)(26,40)(27,37)(28,39)(29,48)(30,46)
(31,47)(32,45)(50,51)(53,59)(54,57)(55,60)(56,58)(61,64);
s3 := Sym(64)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,13)(10,14)(11,15)(12,16)(17,21)
(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)
(41,45)(42,46)(43,47)(44,48)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)
(60,64);
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3 >;

References : None.
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