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Polytope of Type {37}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {37}*74
Also Known As : 37-gon, {37}. if this polytope has another name.
Group : SmallGroup(74,1)
Rank : 2
Schlafli Type : {37}
Number of vertices, edges, etc : 37, 37
Order of s0s1 : 37
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {37,2} of size 148
Vertex Figure Of :
   {2,37} of size 148
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {74}*148
   3-fold covers : {111}*222
   4-fold covers : {148}*296
   5-fold covers : {185}*370
   6-fold covers : {222}*444
   7-fold covers : {259}*518
   8-fold covers : {296}*592
   9-fold covers : {333}*666
   10-fold covers : {370}*740
   11-fold covers : {407}*814
   12-fold covers : {444}*888
   13-fold covers : {481}*962
   14-fold covers : {518}*1036
   15-fold covers : {555}*1110
   16-fold covers : {592}*1184
   17-fold covers : {629}*1258
   18-fold covers : {666}*1332
   19-fold covers : {703}*1406
   20-fold covers : {740}*1480
   21-fold covers : {777}*1554
   22-fold covers : {814}*1628
   23-fold covers : {851}*1702
   24-fold covers : {888}*1776
   25-fold covers : {925}*1850
   26-fold covers : {962}*1924
   27-fold covers : {999}*1998
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)(30,31)(32,33)(34,35)(36,37);;
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)(29,30)(31,32)(33,34)(35,36);;
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*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(37)!( 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)(30,31)(32,33)(34,35)(36,37);
s1 := Sym(37)!( 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)(29,30)(31,32)(33,34)(35,36);
poly := sub<Sym(37)|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*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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