Polytope of Type {3,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,8}*768b
if this polytope has a name.
Group : SmallGroup(768,1086052)
Rank : 4
Schlafli Type : {3,4,8}
Number of vertices, edges, etc : 3, 24, 64, 32
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 : {3,4,4}*384a
   4-fold quotients : {3,4,4}*192a
   16-fold quotients : {3,4,2}*48
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 := ( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)( 9,10)(17,49)(18,50)(19,52)(20,51)
(21,61)(22,62)(23,64)(24,63)(25,58)(26,57)(27,59)(28,60)(29,53)(30,54)(31,56)
(32,55)(35,36)(37,45)(38,46)(39,48)(40,47)(41,42);;
s2 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,27)(10,28)
(11,25)(12,26)(13,32)(14,31)(15,30)(16,29)(33,49)(34,50)(35,51)(36,52)(37,54)
(38,53)(39,56)(40,55)(41,59)(42,60)(43,57)(44,58)(45,64)(46,63)(47,62)
(48,61);;
s3 := ( 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);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1, 
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2 ];;
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)!( 3, 4)( 5,13)( 6,14)( 7,16)( 8,15)( 9,10)(17,49)(18,50)(19,52)
(20,51)(21,61)(22,62)(23,64)(24,63)(25,58)(26,57)(27,59)(28,60)(29,53)(30,54)
(31,56)(32,55)(35,36)(37,45)(38,46)(39,48)(40,47)(41,42);
s2 := Sym(64)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,27)
(10,28)(11,25)(12,26)(13,32)(14,31)(15,30)(16,29)(33,49)(34,50)(35,51)(36,52)
(37,54)(38,53)(39,56)(40,55)(41,59)(42,60)(43,57)(44,58)(45,64)(46,63)(47,62)
(48,61);
s3 := 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);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s0*s2*s1*s0*s2*s1, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2 >;

References : None.
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