Polytope of Type {13}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13}*26
Also Known As : 13-gon, {13}. if this polytope has another name.
Group : SmallGroup(26,1)
Rank : 2
Schlafli Type : {13}
Number of vertices, edges, etc : 13, 13
Order of s₀s₁ : 13
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {13,2} of size 52
   {13,26} of size 676
   {13,3} of size 1092
   {13,6} of size 1092
   {13,7} of size 1092
   {13,7} of size 1092
   {13,7} of size 1092
   {13,13} of size 1092
Vertex Figure Of :
   {2,13} of size 52
   {26,13} of size 676
   {3,13} of size 1092
   {6,13} of size 1092
   {7,13} of size 1092
   {7,13} of size 1092
   {7,13} of size 1092
   {13,13} of size 1092
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {26}*52
   3-fold covers : {39}*78
   4-fold covers : {52}*104
   5-fold covers : {65}*130
   6-fold covers : {78}*156
   7-fold covers : {91}*182
   8-fold covers : {104}*208
   9-fold covers : {117}*234
   10-fold covers : {130}*260
   11-fold covers : {143}*286
   12-fold covers : {156}*312
   13-fold covers : {169}*338
   14-fold covers : {182}*364
   15-fold covers : {195}*390
   16-fold covers : {208}*416
   17-fold covers : {221}*442
   18-fold covers : {234}*468
   19-fold covers : {247}*494
   20-fold covers : {260}*520
   21-fold covers : {273}*546
   22-fold covers : {286}*572
   23-fold covers : {299}*598
   24-fold covers : {312}*624
   25-fold covers : {325}*650
   26-fold covers : {338}*676
   27-fold covers : {351}*702
   28-fold covers : {364}*728
   29-fold covers : {377}*754
   30-fold covers : {390}*780
   31-fold covers : {403}*806
   32-fold covers : {416}*832
   33-fold covers : {429}*858
   34-fold covers : {442}*884
   35-fold covers : {455}*910
   36-fold covers : {468}*936
   37-fold covers : {481}*962
   38-fold covers : {494}*988
   39-fold covers : {507}*1014
   40-fold covers : {520}*1040
   41-fold covers : {533}*1066
   42-fold covers : {546}*1092
   43-fold covers : {559}*1118
   44-fold covers : {572}*1144
   45-fold covers : {585}*1170
   46-fold covers : {598}*1196
   47-fold covers : {611}*1222
   48-fold covers : {624}*1248
   49-fold covers : {637}*1274
   50-fold covers : {650}*1300
   51-fold covers : {663}*1326
   52-fold covers : {676}*1352
   53-fold covers : {689}*1378
   54-fold covers : {702}*1404
   55-fold covers : {715}*1430
   56-fold covers : {728}*1456
   57-fold covers : {741}*1482
   58-fold covers : {754}*1508
   59-fold covers : {767}*1534
   60-fold covers : {780}*1560
   61-fold covers : {793}*1586
   62-fold covers : {806}*1612
   63-fold covers : {819}*1638
   64-fold covers : {832}*1664
   65-fold covers : {845}*1690
   66-fold covers : {858}*1716
   67-fold covers : {871}*1742
   68-fold covers : {884}*1768
   69-fold covers : {897}*1794
   70-fold covers : {910}*1820
   71-fold covers : {923}*1846
   72-fold covers : {936}*1872
   73-fold covers : {949}*1898
   74-fold covers : {962}*1924
   75-fold covers : {975}*1950
   76-fold covers : {988}*1976
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope