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# Polytope of Type {2,2,14}

Atlas Canonical Name : {2,2,14}*112
if this polytope has a name.
Group : SmallGroup(112,42)
Rank : 4
Schlafli Type : {2,2,14}
Number of vertices, edges, etc : 2, 2, 14, 14
Order of s0s1s2s3 : 14
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,14,2} of size 224
{2,2,14,4} of size 448
{2,2,14,6} of size 672
{2,2,14,7} of size 784
{2,2,14,8} of size 896
{2,2,14,10} of size 1120
{2,2,14,12} of size 1344
{2,2,14,4} of size 1568
{2,2,14,14} of size 1568
{2,2,14,14} of size 1568
{2,2,14,14} of size 1568
{2,2,14,16} of size 1792
Vertex Figure Of :
{2,2,2,14} of size 224
{3,2,2,14} of size 336
{4,2,2,14} of size 448
{5,2,2,14} of size 560
{6,2,2,14} of size 672
{7,2,2,14} of size 784
{8,2,2,14} of size 896
{9,2,2,14} of size 1008
{10,2,2,14} of size 1120
{11,2,2,14} of size 1232
{12,2,2,14} of size 1344
{13,2,2,14} of size 1456
{14,2,2,14} of size 1568
{15,2,2,14} of size 1680
{16,2,2,14} of size 1792
{17,2,2,14} of size 1904
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,7}*56
7-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,28}*224, {2,4,14}*224, {4,2,14}*224
3-fold covers : {2,6,14}*336, {6,2,14}*336, {2,2,42}*336
4-fold covers : {2,4,28}*448, {4,2,28}*448, {4,4,14}*448, {2,2,56}*448, {2,8,14}*448, {8,2,14}*448
5-fold covers : {2,10,14}*560, {10,2,14}*560, {2,2,70}*560
6-fold covers : {2,12,14}*672, {12,2,14}*672, {2,6,28}*672a, {6,2,28}*672, {4,6,14}*672a, {6,4,14}*672, {2,2,84}*672, {2,4,42}*672a, {4,2,42}*672
7-fold covers : {2,2,98}*784, {2,14,14}*784a, {2,14,14}*784b, {14,2,14}*784
8-fold covers : {4,4,28}*896, {2,4,56}*896a, {2,4,28}*896, {2,4,56}*896b, {2,8,28}*896a, {2,8,28}*896b, {4,2,56}*896, {8,2,28}*896, {4,8,14}*896a, {8,4,14}*896a, {4,8,14}*896b, {8,4,14}*896b, {4,4,14}*896, {2,2,112}*896, {2,16,14}*896, {16,2,14}*896
9-fold covers : {2,18,14}*1008, {18,2,14}*1008, {2,2,126}*1008, {6,6,14}*1008a, {6,6,14}*1008b, {6,6,14}*1008c, {2,6,42}*1008a, {2,6,42}*1008b, {2,6,42}*1008c, {6,2,42}*1008
10-fold covers : {2,20,14}*1120, {20,2,14}*1120, {2,10,28}*1120, {10,2,28}*1120, {4,10,14}*1120, {10,4,14}*1120, {2,2,140}*1120, {2,4,70}*1120, {4,2,70}*1120
11-fold covers : {2,22,14}*1232, {22,2,14}*1232, {2,2,154}*1232
12-fold covers : {12,2,28}*1344, {4,6,28}*1344a, {4,12,14}*1344a, {12,4,14}*1344, {6,4,28}*1344, {2,24,14}*1344, {24,2,14}*1344, {2,6,56}*1344, {6,2,56}*1344, {6,8,14}*1344, {8,6,14}*1344, {2,12,28}*1344, {2,4,84}*1344a, {4,2,84}*1344, {4,4,42}*1344, {2,2,168}*1344, {2,8,42}*1344, {8,2,42}*1344, {4,6,14}*1344, {6,4,14}*1344, {6,6,14}*1344, {2,6,28}*1344, {2,6,42}*1344, {2,4,42}*1344
13-fold covers : {2,26,14}*1456, {26,2,14}*1456, {2,2,182}*1456
14-fold covers : {2,2,196}*1568, {2,4,98}*1568, {4,2,98}*1568, {2,14,28}*1568a, {2,14,28}*1568b, {2,28,14}*1568a, {14,2,28}*1568, {28,2,14}*1568, {4,14,14}*1568a, {14,4,14}*1568, {4,14,14}*1568c, {2,28,14}*1568c
15-fold covers : {6,10,14}*1680, {10,6,14}*1680, {2,30,14}*1680, {30,2,14}*1680, {2,10,42}*1680, {10,2,42}*1680, {2,6,70}*1680, {6,2,70}*1680, {2,2,210}*1680
16-fold covers : {4,8,14}*1792a, {8,4,14}*1792a, {2,8,28}*1792a, {2,4,56}*1792a, {8,8,14}*1792a, {8,8,14}*1792b, {8,8,14}*1792c, {2,8,56}*1792a, {2,8,56}*1792b, {2,8,56}*1792c, {8,8,14}*1792d, {2,8,56}*1792d, {8,2,56}*1792, {8,4,28}*1792a, {4,4,56}*1792a, {8,4,28}*1792b, {4,4,56}*1792b, {4,8,28}*1792a, {4,4,28}*1792a, {4,4,28}*1792b, {4,8,28}*1792b, {4,8,28}*1792c, {4,8,28}*1792d, {4,16,14}*1792a, {16,4,14}*1792a, {2,16,28}*1792a, {2,4,112}*1792a, {4,16,14}*1792b, {16,4,14}*1792b, {2,16,28}*1792b, {2,4,112}*1792b, {4,4,14}*1792, {4,8,14}*1792b, {8,4,14}*1792b, {2,4,28}*1792, {2,4,56}*1792b, {2,8,28}*1792b, {16,2,28}*1792, {4,2,112}*1792, {2,32,14}*1792, {32,2,14}*1792, {2,2,224}*1792
17-fold covers : {2,34,14}*1904, {34,2,14}*1904, {2,2,238}*1904
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);;
poly := Group([s0,s1,s2,s3]);;

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

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

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

```

to this polytope