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# Polytope of Type {22,4}

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

```
References : None.
to this polytope