Polytope of Type {17}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {17}*34
Also Known As : 17-gon, {17}. if this polytope has another name.
Group : SmallGroup(34,1)
Rank : 2
Schlafli Type : {17}
Number of vertices, edges, etc : 17, 17
Order of s₀s₁ : 17
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {17,2} of size 68
   {17,34} of size 1156
Vertex Figure Of :
   {2,17} of size 68
   {34,17} of size 1156
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {34}*68
   3-fold covers : {51}*102
   4-fold covers : {68}*136
   5-fold covers : {85}*170
   6-fold covers : {102}*204
   7-fold covers : {119}*238
   8-fold covers : {136}*272
   9-fold covers : {153}*306
   10-fold covers : {170}*340
   11-fold covers : {187}*374
   12-fold covers : {204}*408
   13-fold covers : {221}*442
   14-fold covers : {238}*476
   15-fold covers : {255}*510
   16-fold covers : {272}*544
   17-fold covers : {289}*578
   18-fold covers : {306}*612
   19-fold covers : {323}*646
   20-fold covers : {340}*680
   21-fold covers : {357}*714
   22-fold covers : {374}*748
   23-fold covers : {391}*782
   24-fold covers : {408}*816
   25-fold covers : {425}*850
   26-fold covers : {442}*884
   27-fold covers : {459}*918
   28-fold covers : {476}*952
   29-fold covers : {493}*986
   30-fold covers : {510}*1020
   31-fold covers : {527}*1054
   32-fold covers : {544}*1088
   33-fold covers : {561}*1122
   34-fold covers : {578}*1156
   35-fold covers : {595}*1190
   36-fold covers : {612}*1224
   37-fold covers : {629}*1258
   38-fold covers : {646}*1292
   39-fold covers : {663}*1326
   40-fold covers : {680}*1360
   41-fold covers : {697}*1394
   42-fold covers : {714}*1428
   43-fold covers : {731}*1462
   44-fold covers : {748}*1496
   45-fold covers : {765}*1530
   46-fold covers : {782}*1564
   47-fold covers : {799}*1598
   48-fold covers : {816}*1632
   49-fold covers : {833}*1666
   50-fold covers : {850}*1700
   51-fold covers : {867}*1734
   52-fold covers : {884}*1768
   53-fold covers : {901}*1802
   54-fold covers : {918}*1836
   55-fold covers : {935}*1870
   56-fold covers : {952}*1904
   57-fold covers : {969}*1938
   58-fold covers : {986}*1972
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope