Polytope of Type {3,2,2,48}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,48}*1152
if this polytope has a name.
Group : SmallGroup(1152,133451)
Rank : 5
Schlafli Type : {3,2,2,48}
Number of vertices, edges, etc : 3, 3, 2, 48, 48
Order of s₀s₁s₂s₃s₄ : 48
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 : {3,2,2,24}*576
   3-fold quotients : {3,2,2,16}*384
   4-fold quotients : {3,2,2,12}*288
   6-fold quotients : {3,2,2,8}*192
   8-fold quotients : {3,2,2,6}*144
   12-fold quotients : {3,2,2,4}*96
   16-fold quotients : {3,2,2,3}*72
   24-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,20)(18,22)(19,21)(23,26)(24,28)
(25,27)(29,32)(30,34)(31,33)(35,38)(36,40)(37,39)(41,44)(42,46)(43,45)(48,51)
(49,50)(52,53);;
s4 := ( 6,12)( 7, 9)( 8,18)(10,13)(11,15)(14,24)(16,19)(17,21)(20,30)(22,25)
(23,27)(26,36)(28,31)(29,33)(32,42)(34,37)(35,39)(38,48)(40,43)(41,45)(44,52)
(46,49)(47,50)(51,53);;
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, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(53)!(2,3);
s1 := Sym(53)!(1,2);
s2 := Sym(53)!(4,5);
s3 := Sym(53)!( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,20)(18,22)(19,21)(23,26)
(24,28)(25,27)(29,32)(30,34)(31,33)(35,38)(36,40)(37,39)(41,44)(42,46)(43,45)
(48,51)(49,50)(52,53);
s4 := Sym(53)!( 6,12)( 7, 9)( 8,18)(10,13)(11,15)(14,24)(16,19)(17,21)(20,30)
(22,25)(23,27)(26,36)(28,31)(29,33)(32,42)(34,37)(35,39)(38,48)(40,43)(41,45)
(44,52)(46,49)(47,50)(51,53);
poly := sub<Sym(53)|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, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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