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# Polytope of Type {4,22}

Atlas Canonical Name : {4,22}*176
Also Known As : {4,22|2}. if this polytope has another name.
Group : SmallGroup(176,31)
Rank : 3
Schlafli Type : {4,22}
Number of vertices, edges, etc : 4, 44, 22
Order of s0s1s2 : 44
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,22,2} of size 352
{4,22,4} of size 704
{4,22,6} of size 1056
{4,22,8} of size 1408
{4,22,10} of size 1760
{4,22,11} of size 1936
Vertex Figure Of :
{2,4,22} of size 352
{4,4,22} of size 704
{6,4,22} of size 1056
{3,4,22} of size 1056
{8,4,22} of size 1408
{8,4,22} of size 1408
{4,4,22} of size 1408
{6,4,22} of size 1584
{10,4,22} of size 1760
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,22}*88
4-fold quotients : {2,11}*44
11-fold quotients : {4,2}*16
22-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,44}*352, {8,22}*352
3-fold covers : {12,22}*528, {4,66}*528a
4-fold covers : {4,88}*704a, {4,44}*704, {4,88}*704b, {8,44}*704a, {8,44}*704b, {16,22}*704
5-fold covers : {20,22}*880, {4,110}*880
6-fold covers : {24,22}*1056, {12,44}*1056, {4,132}*1056a, {8,66}*1056
7-fold covers : {28,22}*1232, {4,154}*1232
8-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
9-fold covers : {36,22}*1584, {4,198}*1584a, {12,66}*1584a, {12,66}*1584b, {12,66}*1584c, {4,66}*1584
10-fold covers : {40,22}*1760, {20,44}*1760, {4,220}*1760, {8,110}*1760
11-fold covers : {4,242}*1936, {44,22}*1936a, {44,22}*1936c
Permutation Representation (GAP) :
```s0 := (23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)
(33,44);;
s1 := ( 1,23)( 2,33)( 3,32)( 4,31)( 5,30)( 6,29)( 7,28)( 8,27)( 9,26)(10,25)
(11,24)(12,34)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)
(22,35);;
s2 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)(17,19)
(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, 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(44)!(23,34)(24,35)(25,36)(26,37)(27,38)(28,39)(29,40)(30,41)(31,42)
(32,43)(33,44);
s1 := Sym(44)!( 1,23)( 2,33)( 3,32)( 4,31)( 5,30)( 6,29)( 7,28)( 8,27)( 9,26)
(10,25)(11,24)(12,34)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)
(21,36)(22,35);
s2 := Sym(44)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)
(17,19)(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41);
poly := sub<Sym(44)|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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, 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 >;

```
References : None.
to this polytope