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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,6,2}*768
if this polytope has a name.
Group : SmallGroup(768,1076041)
Rank : 5
Schlafli Type : {2,16,6,2}
Number of vertices, edges, etc : 2, 16, 48, 6, 2
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 : {2,8,6,2}*384
   3-fold quotients : {2,16,2,2}*256
   4-fold quotients : {2,4,6,2}*192a
   6-fold quotients : {2,8,2,2}*128
   8-fold quotients : {2,2,6,2}*96
   12-fold quotients : {2,4,2,2}*64
   16-fold quotients : {2,2,3,2}*48
   24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope