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Polytope of Type {6,16,2}

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