Polytope of Type {8,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6,4}*768d
if this polytope has a name.
Group : SmallGroup(768,1090071)
Rank : 4
Schlafli Type : {8,6,4}
Number of vertices, edges, etc : 16, 48, 24, 4
Order of s₀s₁s₂s₃ : 3
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}*192f
   8-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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