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Polytope of Type {34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {34}*68
Also Known As : 34-gon, {34}. if this polytope has another name.
Group : SmallGroup(68,4)
Rank : 2
Schlafli Type : {34}
Number of vertices, edges, etc : 34, 34
Order of s0s1 : 34
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {34,2} of size 136
   {34,4} of size 272
   {34,6} of size 408
   {34,8} of size 544
   {34,10} of size 680
   {34,12} of size 816
   {34,14} of size 952
   {34,16} of size 1088
   {34,17} of size 1156
   {34,18} of size 1224
   {34,20} of size 1360
   {34,22} of size 1496
   {34,24} of size 1632
   {34,26} of size 1768
   {34,28} of size 1904
Vertex Figure Of :
   {2,34} of size 136
   {4,34} of size 272
   {6,34} of size 408
   {8,34} of size 544
   {10,34} of size 680
   {12,34} of size 816
   {14,34} of size 952
   {16,34} of size 1088
   {17,34} of size 1156
   {18,34} of size 1224
   {20,34} of size 1360
   {22,34} of size 1496
   {24,34} of size 1632
   {26,34} of size 1768
   {28,34} of size 1904
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {17}*34
   17-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {68}*136
   3-fold covers : {102}*204
   4-fold covers : {136}*272
   5-fold covers : {170}*340
   6-fold covers : {204}*408
   7-fold covers : {238}*476
   8-fold covers : {272}*544
   9-fold covers : {306}*612
   10-fold covers : {340}*680
   11-fold covers : {374}*748
   12-fold covers : {408}*816
   13-fold covers : {442}*884
   14-fold covers : {476}*952
   15-fold covers : {510}*1020
   16-fold covers : {544}*1088
   17-fold covers : {578}*1156
   18-fold covers : {612}*1224
   19-fold covers : {646}*1292
   20-fold covers : {680}*1360
   21-fold covers : {714}*1428
   22-fold covers : {748}*1496
   23-fold covers : {782}*1564
   24-fold covers : {816}*1632
   25-fold covers : {850}*1700
   26-fold covers : {884}*1768
   27-fold covers : {918}*1836
   28-fold covers : {952}*1904
   29-fold covers : {986}*1972
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28)(29,30)(31,32)(33,34);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)
(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,34);;
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*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(34)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34);
s1 := Sym(34)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)
(18,19)(20,25)(22,23)(24,29)(26,27)(28,33)(30,31)(32,34);
poly := sub<Sym(34)|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*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.
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