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

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

Permutation Representation (Magma) :

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

to this polytope