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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,16,2}*768
if this polytope has a name.
Group : SmallGroup(768,1076041)
Rank : 5
Schlafli Type : {2,6,16,2}
Number of vertices, edges, etc : 2, 6, 48, 16, 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 : {2,6,8,2}*384
   3-fold quotients : {2,2,16,2}*256
   4-fold quotients : {2,6,4,2}*192a
   6-fold quotients : {2,2,8,2}*128
   8-fold quotients : {2,6,2,2}*96
   12-fold quotients : {2,2,4,2}*64
   16-fold quotients : {2,3,2,2}*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 := ( 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);;
s2 := ( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,22)(16,21)(17,23)(18,25)(19,24)
(20,26)(27,46)(28,45)(29,47)(30,49)(31,48)(32,50)(33,40)(34,39)(35,41)(36,43)
(37,42)(38,44);;
s3 := ( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,36)(10,37)(11,38)(12,33)
(13,34)(14,35)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,39)(22,40)(23,41)
(24,42)(25,43)(26,44);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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(52)!(1,2);
s1 := Sym(52)!( 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);
s2 := Sym(52)!( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,22)(16,21)(17,23)(18,25)
(19,24)(20,26)(27,46)(28,45)(29,47)(30,49)(31,48)(32,50)(33,40)(34,39)(35,41)
(36,43)(37,42)(38,44);
s3 := Sym(52)!( 3,27)( 4,28)( 5,29)( 6,30)( 7,31)( 8,32)( 9,36)(10,37)(11,38)
(12,33)(13,34)(14,35)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,39)(22,40)
(23,41)(24,42)(25,43)(26,44);
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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