Polytope of Type {2,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22}*88
if this polytope has a name.
Group : SmallGroup(88,11)
Rank : 3
Schlafli Type : {2,22}
Number of vertices, edges, etc : 2, 22, 22
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 :
   {2,22,2} of size 176
   {2,22,4} of size 352
   {2,22,6} of size 528
   {2,22,8} of size 704
   {2,22,10} of size 880
   {2,22,11} of size 968
   {2,22,12} of size 1056
   {2,22,14} of size 1232
   {2,22,16} of size 1408
   {2,22,18} of size 1584
   {2,22,20} of size 1760
   {2,22,4} of size 1936
   {2,22,22} of size 1936
   {2,22,22} of size 1936
   {2,22,22} of size 1936
Vertex Figure Of :
   {2,2,22} of size 176
   {3,2,22} of size 264
   {4,2,22} of size 352
   {5,2,22} of size 440
   {6,2,22} of size 528
   {7,2,22} of size 616
   {8,2,22} of size 704
   {9,2,22} of size 792
   {10,2,22} of size 880
   {11,2,22} of size 968
   {12,2,22} of size 1056
   {13,2,22} of size 1144
   {14,2,22} of size 1232
   {15,2,22} of size 1320
   {16,2,22} of size 1408
   {17,2,22} of size 1496
   {18,2,22} of size 1584
   {19,2,22} of size 1672
   {20,2,22} of size 1760
   {21,2,22} of size 1848
   {22,2,22} of size 1936
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,11}*44
   11-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,44}*176, {4,22}*176
   3-fold covers : {6,22}*264, {2,66}*264
   4-fold covers : {4,44}*352, {2,88}*352, {8,22}*352
   5-fold covers : {10,22}*440, {2,110}*440
   6-fold covers : {12,22}*528, {6,44}*528a, {2,132}*528, {4,66}*528a
   7-fold covers : {14,22}*616, {2,154}*616
   8-fold covers : {4,88}*704a, {4,44}*704, {4,88}*704b, {8,44}*704a, {8,44}*704b, {2,176}*704, {16,22}*704
   9-fold covers : {18,22}*792, {2,198}*792, {6,66}*792a, {6,66}*792b, {6,66}*792c
   10-fold covers : {20,22}*880, {10,44}*880, {2,220}*880, {4,110}*880
   11-fold covers : {2,242}*968, {22,22}*968a, {22,22}*968b
   12-fold covers : {24,22}*1056, {6,88}*1056, {12,44}*1056, {4,132}*1056a, {2,264}*1056, {8,66}*1056, {6,44}*1056, {6,66}*1056, {4,66}*1056
   13-fold covers : {26,22}*1144, {2,286}*1144
   14-fold covers : {28,22}*1232, {14,44}*1232, {2,308}*1232, {4,154}*1232
   15-fold covers : {30,22}*1320, {10,66}*1320, {6,110}*1320, {2,330}*1320
   16-fold covers : {8,44}*1408a, {4,88}*1408a, {8,88}*1408a, {8,88}*1408b, {8,88}*1408c, {8,88}*1408d, {16,44}*1408a, {4,176}*1408a, {16,44}*1408b, {4,176}*1408b, {4,44}*1408, {4,88}*1408b, {8,44}*1408b, {32,22}*1408, {2,352}*1408
   17-fold covers : {34,22}*1496, {2,374}*1496
   18-fold covers : {36,22}*1584, {18,44}*1584a, {2,396}*1584, {4,198}*1584a, {6,132}*1584a, {12,66}*1584a, {12,66}*1584b, {6,132}*1584b, {6,132}*1584c, {12,66}*1584c, {4,44}*1584, {4,66}*1584, {6,44}*1584
   19-fold covers : {38,22}*1672, {2,418}*1672
   20-fold covers : {40,22}*1760, {10,88}*1760, {20,44}*1760, {4,220}*1760, {2,440}*1760, {8,110}*1760
   21-fold covers : {42,22}*1848, {14,66}*1848, {6,154}*1848, {2,462}*1848
   22-fold covers : {2,484}*1936, {4,242}*1936, {22,44}*1936a, {22,44}*1936b, {44,22}*1936a, {44,22}*1936c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24);;
s2 := ( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)(20,21)
(22,24);;
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*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(24)!(1,2);
s1 := Sym(24)!( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24);
s2 := Sym(24)!( 3, 7)( 4, 5)( 6,11)( 8, 9)(10,15)(12,13)(14,19)(16,17)(18,23)
(20,21)(22,24);
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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope