Polytope of Type {11,2}

This page is part of the Atlas of Small Regular Polytopes
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