Polytope of Type {29}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {29}*58
Also Known As : 29-gon, {29}. if this polytope has another name.
Group : SmallGroup(58,1)
Rank : 2
Schlafli Type : {29}
Number of vertices, edges, etc : 29, 29
Order of s₀s₁ : 29
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {29,2} of size 116
Vertex Figure Of :
   {2,29} of size 116
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {58}*116
   3-fold covers : {87}*174
   4-fold covers : {116}*232
   5-fold covers : {145}*290
   6-fold covers : {174}*348
   7-fold covers : {203}*406
   8-fold covers : {232}*464
   9-fold covers : {261}*522
   10-fold covers : {290}*580
   11-fold covers : {319}*638
   12-fold covers : {348}*696
   13-fold covers : {377}*754
   14-fold covers : {406}*812
   15-fold covers : {435}*870
   16-fold covers : {464}*928
   17-fold covers : {493}*986
   18-fold covers : {522}*1044
   19-fold covers : {551}*1102
   20-fold covers : {580}*1160
   21-fold covers : {609}*1218
   22-fold covers : {638}*1276
   23-fold covers : {667}*1334
   24-fold covers : {696}*1392
   25-fold covers : {725}*1450
   26-fold covers : {754}*1508
   27-fold covers : {783}*1566
   28-fold covers : {812}*1624
   29-fold covers : {841}*1682
   30-fold covers : {870}*1740
   31-fold covers : {899}*1798
   32-fold covers : {928}*1856
   33-fold covers : {957}*1914
   34-fold covers : {986}*1972
Permutation Representation (GAP) :

s0 := ( 2, 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);;
s1 := ( 1, 2)( 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);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!( 2, 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);
s1 := Sym(29)!( 1, 2)( 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);
poly := sub<Sym(29)|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 >;

References : None.
to this polytope