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# Polytope of Type {2,2,14,2}

Atlas Canonical Name : {2,2,14,2}*224
if this polytope has a name.
Group : SmallGroup(224,196)
Rank : 5
Schlafli Type : {2,2,14,2}
Number of vertices, edges, etc : 2, 2, 14, 14, 2
Order of s0s1s2s3s4 : 14
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,14,2,2} of size 448
{2,2,14,2,3} of size 672
{2,2,14,2,4} of size 896
{2,2,14,2,5} of size 1120
{2,2,14,2,6} of size 1344
{2,2,14,2,7} of size 1568
{2,2,14,2,8} of size 1792
Vertex Figure Of :
{2,2,2,14,2} of size 448
{3,2,2,14,2} of size 672
{4,2,2,14,2} of size 896
{5,2,2,14,2} of size 1120
{6,2,2,14,2} of size 1344
{7,2,2,14,2} of size 1568
{8,2,2,14,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,7,2}*112
7-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,28,2}*448, {2,2,14,4}*448, {2,4,14,2}*448, {4,2,14,2}*448
3-fold covers : {2,2,14,6}*672, {2,6,14,2}*672, {6,2,14,2}*672, {2,2,42,2}*672
4-fold covers : {2,2,28,4}*896, {2,4,28,2}*896, {4,2,28,2}*896, {4,4,14,2}*896, {2,4,14,4}*896, {4,2,14,4}*896, {2,2,56,2}*896, {2,2,14,8}*896, {2,8,14,2}*896, {8,2,14,2}*896
5-fold covers : {2,2,14,10}*1120, {2,10,14,2}*1120, {10,2,14,2}*1120, {2,2,70,2}*1120
6-fold covers : {2,2,14,12}*1344, {2,12,14,2}*1344, {12,2,14,2}*1344, {2,2,28,6}*1344a, {2,6,28,2}*1344a, {6,2,28,2}*1344, {2,4,14,6}*1344, {2,6,14,4}*1344, {4,2,14,6}*1344, {4,6,14,2}*1344a, {6,2,14,4}*1344, {6,4,14,2}*1344, {2,2,84,2}*1344, {2,2,42,4}*1344a, {2,4,42,2}*1344a, {4,2,42,2}*1344
7-fold covers : {2,2,98,2}*1568, {2,2,14,14}*1568a, {2,2,14,14}*1568c, {2,14,14,2}*1568a, {2,14,14,2}*1568b, {14,2,14,2}*1568
8-fold covers : {4,4,28,2}*1792, {2,4,28,4}*1792, {4,4,14,4}*1792, {4,2,28,4}*1792, {4,8,14,2}*1792a, {8,4,14,2}*1792a, {2,2,28,8}*1792a, {2,8,28,2}*1792a, {2,2,56,4}*1792a, {2,4,56,2}*1792a, {4,8,14,2}*1792b, {8,4,14,2}*1792b, {2,2,28,8}*1792b, {2,8,28,2}*1792b, {2,2,56,4}*1792b, {2,4,56,2}*1792b, {4,4,14,2}*1792, {2,2,28,4}*1792, {2,4,28,2}*1792, {4,2,14,8}*1792, {8,2,14,4}*1792, {2,4,14,8}*1792, {2,8,14,4}*1792, {8,2,28,2}*1792, {4,2,56,2}*1792, {2,2,14,16}*1792, {2,16,14,2}*1792, {16,2,14,2}*1792, {2,2,112,2}*1792
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s3 := ( 5, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,18);;
s4 := (19,20);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(20)!(1,2);
s1 := Sym(20)!(3,4);
s2 := Sym(20)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s3 := Sym(20)!( 5, 9)( 6, 7)( 8,13)(10,11)(12,17)(14,15)(16,18);
s4 := Sym(20)!(19,20);
poly := sub<Sym(20)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope