Polytope of Type {22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22}*44
Also Known As : 22-gon, {22}. if this polytope has another name.
Group : SmallGroup(44,3)
Rank : 2
Schlafli Type : {22}
Number of vertices, edges, etc : 22, 22
Order of s0s1 : 22
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {22,2} of size 88
   {22,4} of size 176
   {22,6} of size 264
   {22,8} of size 352
   {22,10} of size 440
   {22,11} of size 484
   {22,12} of size 528
   {22,14} of size 616
   {22,16} of size 704
   {22,18} of size 792
   {22,20} of size 880
   {22,4} of size 968
   {22,22} of size 968
   {22,22} of size 968
   {22,22} of size 968
   {22,24} of size 1056
   {22,26} of size 1144
   {22,28} of size 1232
   {22,30} of size 1320
   {22,32} of size 1408
   {22,3} of size 1452
   {22,6} of size 1452
   {22,33} of size 1452
   {22,34} of size 1496
   {22,36} of size 1584
   {22,38} of size 1672
   {22,40} of size 1760
   {22,42} of size 1848
   {22,44} of size 1936
   {22,44} of size 1936
   {22,44} of size 1936
   {22,4} of size 1936
Vertex Figure Of :
   {2,22} of size 88
   {4,22} of size 176
   {6,22} of size 264
   {8,22} of size 352
   {10,22} of size 440
   {11,22} of size 484
   {12,22} of size 528
   {14,22} of size 616
   {16,22} of size 704
   {18,22} of size 792
   {20,22} of size 880
   {4,22} of size 968
   {22,22} of size 968
   {22,22} of size 968
   {22,22} of size 968
   {24,22} of size 1056
   {26,22} of size 1144
   {28,22} of size 1232
   {30,22} of size 1320
   {32,22} of size 1408
   {3,22} of size 1452
   {6,22} of size 1452
   {33,22} of size 1452
   {34,22} of size 1496
   {36,22} of size 1584
   {38,22} of size 1672
   {40,22} of size 1760
   {42,22} of size 1848
   {44,22} of size 1936
   {44,22} of size 1936
   {44,22} of size 1936
   {4,22} of size 1936
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {11}*22
   11-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {44}*88
   3-fold covers : {66}*132
   4-fold covers : {88}*176
   5-fold covers : {110}*220
   6-fold covers : {132}*264
   7-fold covers : {154}*308
   8-fold covers : {176}*352
   9-fold covers : {198}*396
   10-fold covers : {220}*440
   11-fold covers : {242}*484
   12-fold covers : {264}*528
   13-fold covers : {286}*572
   14-fold covers : {308}*616
   15-fold covers : {330}*660
   16-fold covers : {352}*704
   17-fold covers : {374}*748
   18-fold covers : {396}*792
   19-fold covers : {418}*836
   20-fold covers : {440}*880
   21-fold covers : {462}*924
   22-fold covers : {484}*968
   23-fold covers : {506}*1012
   24-fold covers : {528}*1056
   25-fold covers : {550}*1100
   26-fold covers : {572}*1144
   27-fold covers : {594}*1188
   28-fold covers : {616}*1232
   29-fold covers : {638}*1276
   30-fold covers : {660}*1320
   31-fold covers : {682}*1364
   32-fold covers : {704}*1408
   33-fold covers : {726}*1452
   34-fold covers : {748}*1496
   35-fold covers : {770}*1540
   36-fold covers : {792}*1584
   37-fold covers : {814}*1628
   38-fold covers : {836}*1672
   39-fold covers : {858}*1716
   40-fold covers : {880}*1760
   41-fold covers : {902}*1804
   42-fold covers : {924}*1848
   43-fold covers : {946}*1892
   44-fold covers : {968}*1936
   45-fold covers : {990}*1980
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)(18,19)
(20,22);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(22)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22);
s1 := Sym(22)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)
(18,19)(20,22);
poly := sub<Sym(22)|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 >; 
 
References : None.
to this polytope