Polytope of Type {3,2,6,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,6,16}*1152
if this polytope has a name.
Group : SmallGroup(1152,133448)
Rank : 5
Schlafli Type : {3,2,6,16}
Number of vertices, edges, etc : 3, 3, 6, 48, 16
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 : {3,2,6,8}*576
   3-fold quotients : {3,2,2,16}*384
   4-fold quotients : {3,2,6,4}*288a
   6-fold quotients : {3,2,2,8}*192
   8-fold quotients : {3,2,6,2}*144
   12-fold quotients : {3,2,2,4}*96
   16-fold quotients : {3,2,3,2}*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 := ( 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)(50,51);;
s3 := ( 4, 5)( 7, 8)(10,14)(11,13)(12,15)(16,23)(17,22)(18,24)(19,26)(20,25)
(21,27)(28,47)(29,46)(30,48)(31,50)(32,49)(33,51)(34,41)(35,40)(36,42)(37,44)
(38,43)(39,45);;
s4 := ( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,37)(11,38)(12,39)(13,34)
(14,35)(15,36)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,40)(23,41)(24,42)
(25,43)(26,44)(27,45);;
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, 
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(51)!(2,3);
s1 := Sym(51)!(1,2);
s2 := Sym(51)!( 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)(50,51);
s3 := Sym(51)!( 4, 5)( 7, 8)(10,14)(11,13)(12,15)(16,23)(17,22)(18,24)(19,26)
(20,25)(21,27)(28,47)(29,46)(30,48)(31,50)(32,49)(33,51)(34,41)(35,40)(36,42)
(37,44)(38,43)(39,45);
s4 := Sym(51)!( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,37)(11,38)(12,39)
(13,34)(14,35)(15,36)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,40)(23,41)
(24,42)(25,43)(26,44)(27,45);
poly := sub<Sym(51)|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, s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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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