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Polytope of Type {2,16,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,6}*384
if this polytope has a name.
Group : SmallGroup(384,14592)
Rank : 4
Schlafli Type : {2,16,6}
Number of vertices, edges, etc : 2, 16, 48, 6
Order of s0s1s2s3 : 48
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,16,6,2} of size 768
   {2,16,6,3} of size 1152
Vertex Figure Of :
   {2,2,16,6} of size 768
   {3,2,16,6} of size 1152
   {5,2,16,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,8,6}*192
   3-fold quotients : {2,16,2}*128
   4-fold quotients : {2,4,6}*96a
   6-fold quotients : {2,8,2}*64
   8-fold quotients : {2,2,6}*48
   12-fold quotients : {2,4,2}*32
   16-fold quotients : {2,2,3}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,16,6}*768a, {2,16,12}*768a, {2,32,6}*768
   3-fold covers : {2,16,18}*1152, {6,16,6}*1152, {2,48,6}*1152a, {2,48,6}*1152b
   5-fold covers : {2,16,30}*1920, {10,16,6}*1920, {2,80,6}*1920
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);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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(50)!(1,2);
s1 := Sym(50)!( 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(50)!( 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(50)!( 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);
poly := sub<Sym(50)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, 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 >; 
 

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