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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,16}*768
if this polytope has a name.
Group : SmallGroup(768,1076041)
Rank : 5
Schlafli Type : {2,2,6,16}
Number of vertices, edges, etc : 2, 2, 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 : {2,2,6,8}*384
   3-fold quotients : {2,2,2,16}*256
   4-fold quotients : {2,2,6,4}*192a
   6-fold quotients : {2,2,2,8}*128
   8-fold quotients : {2,2,6,2}*96
   12-fold quotients : {2,2,2,4}*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 := (3,4);;
s2 := ( 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)(51,52);;
s3 := ( 5, 6)( 8, 9)(11,15)(12,14)(13,16)(17,24)(18,23)(19,25)(20,27)(21,26)
(22,28)(29,48)(30,47)(31,49)(32,51)(33,50)(34,52)(35,42)(36,41)(37,43)(38,45)
(39,44)(40,46);;
s4 := ( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,38)(12,39)(13,40)(14,35)
(15,36)(16,37)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,41)(24,42)(25,43)
(26,44)(27,45)(28,46);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, 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(52)!(1,2);
s1 := Sym(52)!(3,4);
s2 := Sym(52)!( 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)(51,52);
s3 := Sym(52)!( 5, 6)( 8, 9)(11,15)(12,14)(13,16)(17,24)(18,23)(19,25)(20,27)
(21,26)(22,28)(29,48)(30,47)(31,49)(32,51)(33,50)(34,52)(35,42)(36,41)(37,43)
(38,45)(39,44)(40,46);
s4 := Sym(52)!( 5,29)( 6,30)( 7,31)( 8,32)( 9,33)(10,34)(11,38)(12,39)(13,40)
(14,35)(15,36)(16,37)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,41)(24,42)
(25,43)(26,44)(27,45)(28,46);
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
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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