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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,16,6}*768
if this polytope has a name.
Group : SmallGroup(768,1076041)
Rank : 5
Schlafli Type : {2,2,16,6}
Number of vertices, edges, etc : 2, 2, 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 : {2,2,8,6}*384
   3-fold quotients : {2,2,16,2}*256
   4-fold quotients : {2,2,4,6}*192a
   6-fold quotients : {2,2,8,2}*128
   8-fold quotients : {2,2,2,6}*96
   12-fold quotients : {2,2,4,2}*64
   16-fold quotients : {2,2,2,3}*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 := (11,14)(12,15)(13,16)(17,23)(18,24)(19,25)(20,26)(21,27)(22,28)(29,47)
(30,48)(31,49)(32,50)(33,51)(34,52)(35,41)(36,42)(37,43)(38,44)(39,45)
(40,46);;
s3 := ( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,38)(12,40)(13,39)(14,35)
(15,37)(16,36)(17,47)(18,49)(19,48)(20,50)(21,52)(22,51)(23,41)(24,43)(25,42)
(26,44)(27,46)(28,45);;
s4 := ( 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);;
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, 
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(52)!(1,2);
s1 := Sym(52)!(3,4);
s2 := Sym(52)!(11,14)(12,15)(13,16)(17,23)(18,24)(19,25)(20,26)(21,27)(22,28)
(29,47)(30,48)(31,49)(32,50)(33,51)(34,52)(35,41)(36,42)(37,43)(38,44)(39,45)
(40,46);
s3 := Sym(52)!( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,38)(12,40)(13,39)
(14,35)(15,37)(16,36)(17,47)(18,49)(19,48)(20,50)(21,52)(22,51)(23,41)(24,43)
(25,42)(26,44)(27,46)(28,45);
s4 := Sym(52)!( 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);
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, 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 >; 
 

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