Questions?
See the FAQ
or other info.

# Polytope of Type {11,2}

Atlas Canonical Name : {11,2}*44
if this polytope has a name.
Group : SmallGroup(44,3)
Rank : 3
Schlafli Type : {11,2}
Number of vertices, edges, etc : 11, 11, 2
Order of s0s1s2 : 22
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{11,2,2} of size 88
{11,2,3} of size 132
{11,2,4} of size 176
{11,2,5} of size 220
{11,2,6} of size 264
{11,2,7} of size 308
{11,2,8} of size 352
{11,2,9} of size 396
{11,2,10} of size 440
{11,2,11} of size 484
{11,2,12} of size 528
{11,2,13} of size 572
{11,2,14} of size 616
{11,2,15} of size 660
{11,2,16} of size 704
{11,2,17} of size 748
{11,2,18} of size 792
{11,2,19} of size 836
{11,2,20} of size 880
{11,2,21} of size 924
{11,2,22} of size 968
{11,2,23} of size 1012
{11,2,24} of size 1056
{11,2,25} of size 1100
{11,2,26} of size 1144
{11,2,27} of size 1188
{11,2,28} of size 1232
{11,2,29} of size 1276
{11,2,30} of size 1320
{11,2,31} of size 1364
{11,2,32} of size 1408
{11,2,33} of size 1452
{11,2,34} of size 1496
{11,2,35} of size 1540
{11,2,36} of size 1584
{11,2,37} of size 1628
{11,2,38} of size 1672
{11,2,39} of size 1716
{11,2,40} of size 1760
{11,2,41} of size 1804
{11,2,42} of size 1848
{11,2,43} of size 1892
{11,2,44} of size 1936
{11,2,45} of size 1980
Vertex Figure Of :
{2,11,2} of size 88
{22,11,2} of size 968
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {22,2}*88
3-fold covers : {33,2}*132
4-fold covers : {44,2}*176, {22,4}*176
5-fold covers : {55,2}*220
6-fold covers : {22,6}*264, {66,2}*264
7-fold covers : {77,2}*308
8-fold covers : {44,4}*352, {88,2}*352, {22,8}*352
9-fold covers : {99,2}*396, {33,6}*396
10-fold covers : {22,10}*440, {110,2}*440
11-fold covers : {121,2}*484, {11,22}*484
12-fold covers : {22,12}*528, {44,6}*528a, {132,2}*528, {66,4}*528a, {33,6}*528, {33,4}*528
13-fold covers : {143,2}*572
14-fold covers : {22,14}*616, {154,2}*616
15-fold covers : {165,2}*660
16-fold covers : {88,4}*704a, {44,4}*704, {88,4}*704b, {44,8}*704a, {44,8}*704b, {176,2}*704, {22,16}*704
17-fold covers : {187,2}*748
18-fold covers : {22,18}*792, {198,2}*792, {66,6}*792a, {66,6}*792b, {66,6}*792c
19-fold covers : {209,2}*836
20-fold covers : {22,20}*880, {44,10}*880, {220,2}*880, {110,4}*880
21-fold covers : {231,2}*924
22-fold covers : {242,2}*968, {22,22}*968a, {22,22}*968c
23-fold covers : {253,2}*1012
24-fold covers : {22,24}*1056, {88,6}*1056, {44,12}*1056, {132,4}*1056a, {264,2}*1056, {66,8}*1056, {33,12}*1056, {33,8}*1056, {44,6}*1056, {66,6}*1056, {66,4}*1056
25-fold covers : {275,2}*1100, {55,10}*1100
26-fold covers : {22,26}*1144, {286,2}*1144
27-fold covers : {297,2}*1188, {99,6}*1188, {33,6}*1188
28-fold covers : {22,28}*1232, {44,14}*1232, {308,2}*1232, {154,4}*1232
29-fold covers : {319,2}*1276
30-fold covers : {22,30}*1320, {66,10}*1320, {110,6}*1320, {330,2}*1320
31-fold covers : {341,2}*1364
32-fold covers : {44,8}*1408a, {88,4}*1408a, {88,8}*1408a, {88,8}*1408b, {88,8}*1408c, {88,8}*1408d, {44,16}*1408a, {176,4}*1408a, {44,16}*1408b, {176,4}*1408b, {44,4}*1408, {88,4}*1408b, {44,8}*1408b, {22,32}*1408, {352,2}*1408
33-fold covers : {363,2}*1452, {33,22}*1452
34-fold covers : {22,34}*1496, {374,2}*1496
35-fold covers : {385,2}*1540
36-fold covers : {22,36}*1584, {44,18}*1584a, {396,2}*1584, {198,4}*1584a, {99,4}*1584, {132,6}*1584a, {66,12}*1584a, {66,12}*1584b, {132,6}*1584b, {132,6}*1584c, {66,12}*1584c, {44,4}*1584, {66,4}*1584, {33,12}*1584, {33,6}*1584, {44,6}*1584
37-fold covers : {407,2}*1628
38-fold covers : {22,38}*1672, {418,2}*1672
39-fold covers : {429,2}*1716
40-fold covers : {22,40}*1760, {88,10}*1760, {44,20}*1760, {220,4}*1760, {440,2}*1760, {110,8}*1760
41-fold covers : {451,2}*1804
42-fold covers : {22,42}*1848, {66,14}*1848, {154,6}*1848, {462,2}*1848
43-fold covers : {473,2}*1892
44-fold covers : {484,2}*1936, {242,4}*1936, {22,44}*1936a, {44,22}*1936a, {44,22}*1936b, {22,44}*1936c
45-fold covers : {495,2}*1980, {165,6}*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);;
s2 := (12,13);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2,
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(13)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11);
s1 := Sym(13)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
s2 := Sym(13)!(12,13);
poly := sub<Sym(13)|s0,s1,s2>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope