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Polytope of Type {16,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,6,2}*384
if this polytope has a name.
Group : SmallGroup(384,14592)
Rank : 4
Schlafli Type : {16,6,2}
Number of vertices, edges, etc : 16, 48, 6, 2
Order of s0s1s2s3 : 48
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {16,6,2,2} of size 768
   {16,6,2,3} of size 1152
   {16,6,2,5} of size 1920
Vertex Figure Of :
   {2,16,6,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,6,2}*192
   3-fold quotients : {16,2,2}*128
   4-fold quotients : {4,6,2}*96a
   6-fold quotients : {8,2,2}*64
   8-fold quotients : {2,6,2}*48
   12-fold quotients : {4,2,2}*32
   16-fold quotients : {2,3,2}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,12,2}*768a, {16,6,4}*768a, {32,6,2}*768
   3-fold covers : {16,18,2}*1152, {16,6,6}*1152a, {16,6,6}*1152b, {48,6,2}*1152a, {48,6,2}*1152b
   5-fold covers : {16,30,2}*1920, {16,6,10}*1920, {80,6,2}*1920
Permutation Representation (GAP) :
s0 := ( 7,10)( 8,11)( 9,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,43)
(26,44)(27,45)(28,46)(29,47)(30,48)(31,37)(32,38)(33,39)(34,40)(35,41)
(36,42);;
s1 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,34)( 8,36)( 9,35)(10,31)
(11,33)(12,32)(13,43)(14,45)(15,44)(16,46)(17,48)(18,47)(19,37)(20,39)(21,38)
(22,40)(23,42)(24,41);;
s2 := ( 1, 2)( 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);;
s3 := (49,50);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(50)!( 7,10)( 8,11)( 9,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)
(25,43)(26,44)(27,45)(28,46)(29,47)(30,48)(31,37)(32,38)(33,39)(34,40)(35,41)
(36,42);
s1 := Sym(50)!( 1,25)( 2,27)( 3,26)( 4,28)( 5,30)( 6,29)( 7,34)( 8,36)( 9,35)
(10,31)(11,33)(12,32)(13,43)(14,45)(15,44)(16,46)(17,48)(18,47)(19,37)(20,39)
(21,38)(22,40)(23,42)(24,41);
s2 := Sym(50)!( 1, 2)( 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);
s3 := Sym(50)!(49,50);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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