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# Polytope of Type {14,4,2}

Atlas Canonical Name : {14,4,2}*224
if this polytope has a name.
Group : SmallGroup(224,178)
Rank : 4
Schlafli Type : {14,4,2}
Number of vertices, edges, etc : 14, 28, 4, 2
Order of s0s1s2s3 : 28
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{14,4,2,2} of size 448
{14,4,2,3} of size 672
{14,4,2,4} of size 896
{14,4,2,5} of size 1120
{14,4,2,6} of size 1344
{14,4,2,7} of size 1568
{14,4,2,8} of size 1792
Vertex Figure Of :
{2,14,4,2} of size 448
{4,14,4,2} of size 896
{6,14,4,2} of size 1344
{7,14,4,2} of size 1568
{8,14,4,2} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {14,2,2}*112
4-fold quotients : {7,2,2}*56
7-fold quotients : {2,4,2}*32
14-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {28,4,2}*448, {14,4,4}*448, {14,8,2}*448
3-fold covers : {14,12,2}*672, {14,4,6}*672, {42,4,2}*672a
4-fold covers : {28,4,4}*896, {56,4,2}*896a, {28,4,2}*896, {56,4,2}*896b, {28,8,2}*896a, {28,8,2}*896b, {14,4,8}*896a, {14,8,4}*896a, {14,4,8}*896b, {14,8,4}*896b, {14,4,4}*896, {14,16,2}*896
5-fold covers : {14,20,2}*1120, {14,4,10}*1120, {70,4,2}*1120
6-fold covers : {14,4,12}*1344, {14,12,4}*1344a, {28,4,6}*1344, {14,24,2}*1344, {14,8,6}*1344, {28,12,2}*1344, {84,4,2}*1344a, {42,4,4}*1344, {42,8,2}*1344
7-fold covers : {98,4,2}*1568, {14,28,2}*1568a, {14,4,14}*1568, {14,28,2}*1568c
8-fold covers : {14,4,8}*1792a, {14,8,4}*1792a, {28,8,2}*1792a, {56,4,2}*1792a, {14,8,8}*1792a, {14,8,8}*1792b, {14,8,8}*1792c, {56,8,2}*1792a, {56,8,2}*1792b, {56,8,2}*1792c, {14,8,8}*1792d, {56,8,2}*1792d, {28,4,8}*1792a, {56,4,4}*1792a, {28,4,8}*1792b, {56,4,4}*1792b, {28,8,4}*1792a, {28,4,4}*1792a, {28,4,4}*1792b, {28,8,4}*1792b, {28,8,4}*1792c, {28,8,4}*1792d, {14,4,16}*1792a, {14,16,4}*1792a, {28,16,2}*1792a, {112,4,2}*1792a, {14,4,16}*1792b, {14,16,4}*1792b, {28,16,2}*1792b, {112,4,2}*1792b, {14,4,4}*1792, {14,4,8}*1792b, {14,8,4}*1792b, {28,4,2}*1792, {56,4,2}*1792b, {28,8,2}*1792b, {14,32,2}*1792
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28);;
s1 := ( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)(18,23)
(20,21)(22,26)(24,27);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)(16,22)
(19,23)(20,24)(25,27)(26,28);;
s3 := (29,30);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
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 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(30)!( 3, 4)( 6, 7)( 8, 9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,24)(25,26)(27,28);
s1 := Sym(30)!( 1, 3)( 2,11)( 4, 8)( 5, 6)( 7,19)( 9,15)(10,17)(12,13)(14,25)
(18,23)(20,21)(22,26)(24,27);
s2 := Sym(30)!( 1, 2)( 3, 6)( 4, 7)( 5,10)( 8,13)( 9,14)(11,17)(12,18)(15,21)
(16,22)(19,23)(20,24)(25,27)(26,28);
s3 := Sym(30)!(29,30);
poly := sub<Sym(30)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, 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 >;

```

to this polytope