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