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Polytope of Type {2,6,16}

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

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