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Polytope of Type {51}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {51}*102
Also Known As : 51-gon, {51}. if this polytope has another name.
Group : SmallGroup(102,3)
Rank : 2
Schlafli Type : {51}
Number of vertices, edges, etc : 51, 51
Order of s0s1 : 51
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {51,2} of size 204
   {51,4} of size 408
   {51,6} of size 612
   {51,6} of size 816
   {51,4} of size 816
   {51,12} of size 1632
   {51,8} of size 1632
   {51,6} of size 1836
Vertex Figure Of :
   {2,51} of size 204
   {4,51} of size 408
   {6,51} of size 612
   {6,51} of size 816
   {4,51} of size 816
   {12,51} of size 1632
   {8,51} of size 1632
   {6,51} of size 1836
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {17}*34
   17-fold quotients : {3}*6
Covers (Minimal Covers in Boldface) :
   2-fold covers : {102}*204
   3-fold covers : {153}*306
   4-fold covers : {204}*408
   5-fold covers : {255}*510
   6-fold covers : {306}*612
   7-fold covers : {357}*714
   8-fold covers : {408}*816
   9-fold covers : {459}*918
   10-fold covers : {510}*1020
   11-fold covers : {561}*1122
   12-fold covers : {612}*1224
   13-fold covers : {663}*1326
   14-fold covers : {714}*1428
   15-fold covers : {765}*1530
   16-fold covers : {816}*1632
   17-fold covers : {867}*1734
   18-fold covers : {918}*1836
   19-fold covers : {969}*1938
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)(38,39)(40,41)(42,43)
(44,45)(46,47)(48,49)(50,51);;
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)(37,38)(39,40)(41,42)
(43,44)(45,46)(47,48)(49,50);;
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*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(51)!( 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)(38,39)(40,41)
(42,43)(44,45)(46,47)(48,49)(50,51);
s1 := Sym(51)!( 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)(37,38)(39,40)
(41,42)(43,44)(45,46)(47,48)(49,50);
poly := sub<Sym(51)|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*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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