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Polytope of Type {3,2,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,16}*192
if this polytope has a name.
Group : SmallGroup(192,469)
Rank : 4
Schlafli Type : {3,2,16}
Number of vertices, edges, etc : 3, 3, 16, 16
Order of s0s1s2s3 : 48
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,16,2} of size 384
   {3,2,16,4} of size 768
   {3,2,16,4} of size 768
   {3,2,16,6} of size 1152
   {3,2,16,10} of size 1920
Vertex Figure Of :
   {2,3,2,16} of size 384
   {3,3,2,16} of size 768
   {4,3,2,16} of size 768
   {6,3,2,16} of size 1152
   {5,3,2,16} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,8}*96
   4-fold quotients : {3,2,4}*48
   8-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,32}*384, {6,2,16}*384
   3-fold covers : {9,2,16}*576, {3,2,48}*576, {3,6,16}*576
   4-fold covers : {3,2,64}*768, {6,4,16}*768a, {12,2,16}*768, {6,2,32}*768, {3,4,16}*768
   5-fold covers : {3,2,80}*960, {15,2,16}*960
   6-fold covers : {9,2,32}*1152, {3,6,32}*1152, {3,2,96}*1152, {18,2,16}*1152, {6,6,16}*1152b, {6,6,16}*1152c, {6,2,48}*1152
   7-fold covers : {3,2,112}*1344, {21,2,16}*1344
   9-fold covers : {27,2,16}*1728, {3,2,144}*1728, {9,2,48}*1728, {3,6,48}*1728a, {9,6,16}*1728, {3,6,16}*1728a, {3,6,48}*1728b, {3,6,16}*1728b
   10-fold covers : {15,2,32}*1920, {3,2,160}*1920, {30,2,16}*1920, {6,10,16}*1920, {6,2,80}*1920
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s3 := ( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1, 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(19)!(2,3);
s1 := Sym(19)!(1,2);
s2 := Sym(19)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s3 := Sym(19)!( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);
poly := sub<Sym(19)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1, 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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