Polytope of Type {19}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {19}*38
Also Known As : 19-gon, {19}. if this polytope has another name.
Group : SmallGroup(38,1)
Rank : 2
Schlafli Type : {19}
Number of vertices, edges, etc : 19, 19
Order of s₀s₁ : 19
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {19,2} of size 76
   {19,38} of size 1444
Vertex Figure Of :
   {2,19} of size 76
   {38,19} of size 1444
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {38}*76
   3-fold covers : {57}*114
   4-fold covers : {76}*152
   5-fold covers : {95}*190
   6-fold covers : {114}*228
   7-fold covers : {133}*266
   8-fold covers : {152}*304
   9-fold covers : {171}*342
   10-fold covers : {190}*380
   11-fold covers : {209}*418
   12-fold covers : {228}*456
   13-fold covers : {247}*494
   14-fold covers : {266}*532
   15-fold covers : {285}*570
   16-fold covers : {304}*608
   17-fold covers : {323}*646
   18-fold covers : {342}*684
   19-fold covers : {361}*722
   20-fold covers : {380}*760
   21-fold covers : {399}*798
   22-fold covers : {418}*836
   23-fold covers : {437}*874
   24-fold covers : {456}*912
   25-fold covers : {475}*950
   26-fold covers : {494}*988
   27-fold covers : {513}*1026
   28-fold covers : {532}*1064
   29-fold covers : {551}*1102
   30-fold covers : {570}*1140
   31-fold covers : {589}*1178
   32-fold covers : {608}*1216
   33-fold covers : {627}*1254
   34-fold covers : {646}*1292
   35-fold covers : {665}*1330
   36-fold covers : {684}*1368
   37-fold covers : {703}*1406
   38-fold covers : {722}*1444
   39-fold covers : {741}*1482
   40-fold covers : {760}*1520
   41-fold covers : {779}*1558
   42-fold covers : {798}*1596
   43-fold covers : {817}*1634
   44-fold covers : {836}*1672
   45-fold covers : {855}*1710
   46-fold covers : {874}*1748
   47-fold covers : {893}*1786
   48-fold covers : {912}*1824
   49-fold covers : {931}*1862
   50-fold covers : {950}*1900
   51-fold covers : {969}*1938
   52-fold covers : {988}*1976
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(19)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19);
s1 := Sym(19)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
poly := sub<Sym(19)|s0,s1>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope