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Polytope of Type {21}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {21}*42
Also Known As : 21-gon, {21}. if this polytope has another name.
Group : SmallGroup(42,5)
Rank : 2
Schlafli Type : {21}
Number of vertices, edges, etc : 21, 21
Order of s0s1 : 21
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {21,2} of size 84
   {21,4} of size 168
   {21,6} of size 252
   {21,6} of size 336
   {21,4} of size 336
   {21,14} of size 588
   {21,12} of size 672
   {21,8} of size 672
   {21,6} of size 756
   {21,10} of size 840
   {21,3} of size 1008
   {21,6} of size 1008
   {21,8} of size 1008
   {21,8} of size 1008
   {21,12} of size 1008
   {21,6} of size 1008
   {21,6} of size 1344
   {21,8} of size 1344
   {21,10} of size 1680
   {21,42} of size 1764
Vertex Figure Of :
   {2,21} of size 84
   {4,21} of size 168
   {6,21} of size 252
   {6,21} of size 336
   {4,21} of size 336
   {14,21} of size 588
   {12,21} of size 672
   {8,21} of size 672
   {6,21} of size 756
   {10,21} of size 840
   {3,21} of size 1008
   {6,21} of size 1008
   {8,21} of size 1008
   {8,21} of size 1008
   {12,21} of size 1008
   {6,21} of size 1008
   {6,21} of size 1344
   {8,21} of size 1344
   {10,21} of size 1680
   {42,21} of size 1764
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {7}*14
   7-fold quotients : {3}*6
Covers (Minimal Covers in Boldface) :
   2-fold covers : {42}*84
   3-fold covers : {63}*126
   4-fold covers : {84}*168
   5-fold covers : {105}*210
   6-fold covers : {126}*252
   7-fold covers : {147}*294
   8-fold covers : {168}*336
   9-fold covers : {189}*378
   10-fold covers : {210}*420
   11-fold covers : {231}*462
   12-fold covers : {252}*504
   13-fold covers : {273}*546
   14-fold covers : {294}*588
   15-fold covers : {315}*630
   16-fold covers : {336}*672
   17-fold covers : {357}*714
   18-fold covers : {378}*756
   19-fold covers : {399}*798
   20-fold covers : {420}*840
   21-fold covers : {441}*882
   22-fold covers : {462}*924
   23-fold covers : {483}*966
   24-fold covers : {504}*1008
   25-fold covers : {525}*1050
   26-fold covers : {546}*1092
   27-fold covers : {567}*1134
   28-fold covers : {588}*1176
   29-fold covers : {609}*1218
   30-fold covers : {630}*1260
   31-fold covers : {651}*1302
   32-fold covers : {672}*1344
   33-fold covers : {693}*1386
   34-fold covers : {714}*1428
   35-fold covers : {735}*1470
   36-fold covers : {756}*1512
   37-fold covers : {777}*1554
   38-fold covers : {798}*1596
   39-fold covers : {819}*1638
   40-fold covers : {840}*1680
   41-fold covers : {861}*1722
   42-fold covers : {882}*1764
   43-fold covers : {903}*1806
   44-fold covers : {924}*1848
   45-fold covers : {945}*1890
   46-fold covers : {966}*1932
   47-fold covers : {987}*1974
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(21)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)
(20,21);
s1 := Sym(21)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20);
poly := sub<Sym(21)|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 >; 
 
References : None.
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