Polytope of Type {11}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {11}*22
Also Known As : endecagon, {11}. if this polytope has another name.
Group : SmallGroup(22,1)
Rank : 2
Schlafli Type : {11}
Number of vertices, edges, etc : 11, 11
Order of s₀s₁ : 11
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {11,2} of size 44
   {11,22} of size 484
   {11,3} of size 1320
   {11,4} of size 1320
   {11,5} of size 1320
   {11,5} of size 1320
   {11,6} of size 1320
   {11,10} of size 1320
   {11,10} of size 1320
   {11,11} of size 1320
   {11,12} of size 1320
   {11,12} of size 1320
Vertex Figure Of :
   {2,11} of size 44
   {22,11} of size 484
   {3,11} of size 1320
   {4,11} of size 1320
   {5,11} of size 1320
   {5,11} of size 1320
   {6,11} of size 1320
   {10,11} of size 1320
   {10,11} of size 1320
   {11,11} of size 1320
   {12,11} of size 1320
   {12,11} of size 1320
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {22}*44
   3-fold covers : {33}*66
   4-fold covers : {44}*88
   5-fold covers : {55}*110
   6-fold covers : {66}*132
   7-fold covers : {77}*154
   8-fold covers : {88}*176
   9-fold covers : {99}*198
   10-fold covers : {110}*220
   11-fold covers : {121}*242
   12-fold covers : {132}*264
   13-fold covers : {143}*286
   14-fold covers : {154}*308
   15-fold covers : {165}*330
   16-fold covers : {176}*352
   17-fold covers : {187}*374
   18-fold covers : {198}*396
   19-fold covers : {209}*418
   20-fold covers : {220}*440
   21-fold covers : {231}*462
   22-fold covers : {242}*484
   23-fold covers : {253}*506
   24-fold covers : {264}*528
   25-fold covers : {275}*550
   26-fold covers : {286}*572
   27-fold covers : {297}*594
   28-fold covers : {308}*616
   29-fold covers : {319}*638
   30-fold covers : {330}*660
   31-fold covers : {341}*682
   32-fold covers : {352}*704
   33-fold covers : {363}*726
   34-fold covers : {374}*748
   35-fold covers : {385}*770
   36-fold covers : {396}*792
   37-fold covers : {407}*814
   38-fold covers : {418}*836
   39-fold covers : {429}*858
   40-fold covers : {440}*880
   41-fold covers : {451}*902
   42-fold covers : {462}*924
   43-fold covers : {473}*946
   44-fold covers : {484}*968
   45-fold covers : {495}*990
   46-fold covers : {506}*1012
   47-fold covers : {517}*1034
   48-fold covers : {528}*1056
   49-fold covers : {539}*1078
   50-fold covers : {550}*1100
   51-fold covers : {561}*1122
   52-fold covers : {572}*1144
   53-fold covers : {583}*1166
   54-fold covers : {594}*1188
   55-fold covers : {605}*1210
   56-fold covers : {616}*1232
   57-fold covers : {627}*1254
   58-fold covers : {638}*1276
   59-fold covers : {649}*1298
   60-fold covers : {660}*1320
   61-fold covers : {671}*1342
   62-fold covers : {682}*1364
   63-fold covers : {693}*1386
   64-fold covers : {704}*1408
   65-fold covers : {715}*1430
   66-fold covers : {726}*1452
   67-fold covers : {737}*1474
   68-fold covers : {748}*1496
   69-fold covers : {759}*1518
   70-fold covers : {770}*1540
   71-fold covers : {781}*1562
   72-fold covers : {792}*1584
   73-fold covers : {803}*1606
   74-fold covers : {814}*1628
   75-fold covers : {825}*1650
   76-fold covers : {836}*1672
   77-fold covers : {847}*1694
   78-fold covers : {858}*1716
   79-fold covers : {869}*1738
   80-fold covers : {880}*1760
   81-fold covers : {891}*1782
   82-fold covers : {902}*1804
   83-fold covers : {913}*1826
   84-fold covers : {924}*1848
   85-fold covers : {935}*1870
   86-fold covers : {946}*1892
   87-fold covers : {957}*1914
   88-fold covers : {968}*1936
   89-fold covers : {979}*1958
   90-fold covers : {990}*1980
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope