Polytope of Type {4,2,3,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,3,8}*768
if this polytope has a name.
Group : SmallGroup(768,1089307)
Rank : 5
Schlafli Type : {4,2,3,8}
Number of vertices, edges, etc : 4, 4, 6, 24, 16
Order of s₀s₁s₂s₃s₄ : 12
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {4,2,3,4}*384, {2,2,3,8}*384
   4-fold quotients : {4,2,3,4}*192, {2,2,3,4}*192
   8-fold quotients : {4,2,3,2}*96, {2,2,3,4}*96
   16-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 8, 9)(10,23)(11,26)(13,18)(14,17)(15,35)(16,38)(19,41)(20,42)
(21,27)(22,24)(25,46)(28,45)(29,30)(31,47)(32,49)(33,36)(34,39)(37,51)(40,52)
(43,44);;
s3 := ( 5, 8)( 6,17)( 7,13)(10,46)(11,45)(12,29)(14,18)(15,51)(16,52)(19,44)
(20,43)(21,28)(22,25)(23,24)(26,27)(31,48)(32,50)(33,37)(34,40)(35,36)(38,39)
(41,42);;
s4 := ( 5,48)( 6,44)( 7,43)( 8,51)( 9,37)(10,38)(11,35)(12,50)(13,46)(14,28)
(15,26)(16,23)(17,45)(18,25)(19,39)(20,36)(21,49)(22,47)(24,31)(27,32)(29,52)
(30,40)(33,42)(34,41);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(52)!(2,3);
s1 := Sym(52)!(1,2)(3,4);
s2 := Sym(52)!( 6, 7)( 8, 9)(10,23)(11,26)(13,18)(14,17)(15,35)(16,38)(19,41)
(20,42)(21,27)(22,24)(25,46)(28,45)(29,30)(31,47)(32,49)(33,36)(34,39)(37,51)
(40,52)(43,44);
s3 := Sym(52)!( 5, 8)( 6,17)( 7,13)(10,46)(11,45)(12,29)(14,18)(15,51)(16,52)
(19,44)(20,43)(21,28)(22,25)(23,24)(26,27)(31,48)(32,50)(33,37)(34,40)(35,36)
(38,39)(41,42);
s4 := Sym(52)!( 5,48)( 6,44)( 7,43)( 8,51)( 9,37)(10,38)(11,35)(12,50)(13,46)
(14,28)(15,26)(16,23)(17,45)(18,25)(19,39)(20,36)(21,49)(22,47)(24,31)(27,32)
(29,52)(30,40)(33,42)(34,41);
poly := sub<Sym(52)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3 >;

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