Polytope of Type {6,4,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,8}*768b
if this polytope has a name.
Group : SmallGroup(768,323566)
Rank : 4
Schlafli Type : {6,4,8}
Number of vertices, edges, etc : 6, 24, 32, 16
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   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 : {6,4,4}*384a
   3-fold quotients : {2,4,8}*256b
   4-fold quotients : {6,4,4}*192
   6-fold quotients : {2,4,4}*128
   8-fold quotients : {6,2,4}*96, {6,4,2}*96a
   12-fold quotients : {2,4,4}*64
   16-fold quotients : {3,2,4}*48, {6,2,2}*48
   24-fold quotients : {2,2,4}*32, {2,4,2}*32
   32-fold quotients : {3,2,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(48)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)
(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48);
s1 := Sym(48)!( 1, 3)( 4, 6)( 7, 9)(10,12)(13,24)(14,23)(15,22)(16,21)(17,20)
(18,19)(25,27)(28,30)(31,33)(34,36)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43);
s2 := Sym(48)!( 7,10)( 8,11)( 9,12)(19,22)(20,23)(21,24)(25,37)(26,38)(27,39)
(28,40)(29,41)(30,42)(31,46)(32,47)(33,48)(34,43)(35,44)(36,45);
s3 := Sym(48)!( 1,25)( 2,26)( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)
(10,34)(11,35)(12,36)(13,46)(14,47)(15,48)(16,43)(17,44)(18,45)(19,40)(20,41)
(21,42)(22,37)(23,38)(24,39);
poly := sub<Sym(48)|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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;

References : None.
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