Polytope of Type {22,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,2}*88
if this polytope has a name.
Group : SmallGroup(88,11)
Rank : 3
Schlafli Type : {22,2}
Number of vertices, edges, etc : 22, 22, 2
Order of s₀s₁s₂ : 22
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {22,2,2} of size 176
   {22,2,3} of size 264
   {22,2,4} of size 352
   {22,2,5} of size 440
   {22,2,6} of size 528
   {22,2,7} of size 616
   {22,2,8} of size 704
   {22,2,9} of size 792
   {22,2,10} of size 880
   {22,2,11} of size 968
   {22,2,12} of size 1056
   {22,2,13} of size 1144
   {22,2,14} of size 1232
   {22,2,15} of size 1320
   {22,2,16} of size 1408
   {22,2,17} of size 1496
   {22,2,18} of size 1584
   {22,2,19} of size 1672
   {22,2,20} of size 1760
   {22,2,21} of size 1848
   {22,2,22} of size 1936
Vertex Figure Of :
   {2,22,2} of size 176
   {4,22,2} of size 352
   {6,22,2} of size 528
   {8,22,2} of size 704
   {10,22,2} of size 880
   {11,22,2} of size 968
   {12,22,2} of size 1056
   {14,22,2} of size 1232
   {16,22,2} of size 1408
   {18,22,2} of size 1584
   {20,22,2} of size 1760
   {4,22,2} of size 1936
   {22,22,2} of size 1936
   {22,22,2} of size 1936
   {22,22,2} of size 1936
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {11,2}*44
   11-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {44,2}*176, {22,4}*176
   3-fold covers : {22,6}*264, {66,2}*264
   4-fold covers : {44,4}*352, {88,2}*352, {22,8}*352
   5-fold covers : {22,10}*440, {110,2}*440
   6-fold covers : {22,12}*528, {44,6}*528a, {132,2}*528, {66,4}*528a
   7-fold covers : {22,14}*616, {154,2}*616
   8-fold covers : {88,4}*704a, {44,4}*704, {88,4}*704b, {44,8}*704a, {44,8}*704b, {176,2}*704, {22,16}*704
   9-fold covers : {22,18}*792, {198,2}*792, {66,6}*792a, {66,6}*792b, {66,6}*792c
   10-fold covers : {22,20}*880, {44,10}*880, {220,2}*880, {110,4}*880
   11-fold covers : {242,2}*968, {22,22}*968a, {22,22}*968c
   12-fold covers : {22,24}*1056, {88,6}*1056, {44,12}*1056, {132,4}*1056a, {264,2}*1056, {66,8}*1056, {44,6}*1056, {66,6}*1056, {66,4}*1056
   13-fold covers : {22,26}*1144, {286,2}*1144
   14-fold covers : {22,28}*1232, {44,14}*1232, {308,2}*1232, {154,4}*1232
   15-fold covers : {22,30}*1320, {66,10}*1320, {110,6}*1320, {330,2}*1320
   16-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
   17-fold covers : {22,34}*1496, {374,2}*1496
   18-fold covers : {22,36}*1584, {44,18}*1584a, {396,2}*1584, {198,4}*1584a, {132,6}*1584a, {66,12}*1584a, {66,12}*1584b, {132,6}*1584b, {132,6}*1584c, {66,12}*1584c, {44,4}*1584, {66,4}*1584, {44,6}*1584
   19-fold covers : {22,38}*1672, {418,2}*1672
   20-fold covers : {22,40}*1760, {88,10}*1760, {44,20}*1760, {220,4}*1760, {440,2}*1760, {110,8}*1760
   21-fold covers : {22,42}*1848, {66,14}*1848, {154,6}*1848, {462,2}*1848
   22-fold covers : {484,2}*1936, {242,4}*1936, {22,44}*1936a, {44,22}*1936a, {44,22}*1936b, {22,44}*1936c
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);;
s2 := (23,24);;
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*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(24)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22);
s1 := Sym(24)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,21)
(18,19)(20,22);
s2 := Sym(24)!(23,24);
poly := sub<Sym(24)|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*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