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Polytope of Type {28,2,2}

Atlas Canonical Name : {28,2,2}*224
if this polytope has a name.
Group : SmallGroup(224,176)
Rank : 4
Schlafli Type : {28,2,2}
Number of vertices, edges, etc : 28, 28, 2, 2
Order of s0s1s2s3 : 28
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{28,2,2,2} of size 448
{28,2,2,3} of size 672
{28,2,2,4} of size 896
{28,2,2,5} of size 1120
{28,2,2,6} of size 1344
{28,2,2,7} of size 1568
{28,2,2,8} of size 1792
Vertex Figure Of :
{2,28,2,2} of size 448
{4,28,2,2} of size 896
{6,28,2,2} of size 1344
{6,28,2,2} of size 1344
{8,28,2,2} of size 1792
{8,28,2,2} of size 1792
{4,28,2,2} 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 : {4,2,2}*32
14-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {28,4,2}*448, {28,2,4}*448, {56,2,2}*448
3-fold covers : {28,2,6}*672, {28,6,2}*672a, {84,2,2}*672
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, {56,2,4}*896, {28,2,8}*896, {112,2,2}*896
5-fold covers : {28,2,10}*1120, {28,10,2}*1120, {140,2,2}*1120
6-fold covers : {28,2,12}*1344, {28,6,4}*1344a, {28,4,6}*1344, {56,2,6}*1344, {56,6,2}*1344, {28,12,2}*1344, {84,4,2}*1344a, {84,2,4}*1344, {168,2,2}*1344
7-fold covers : {196,2,2}*1568, {28,2,14}*1568, {28,14,2}*1568a, {28,14,2}*1568b
8-fold covers : {28,8,2}*1792a, {56,4,2}*1792a, {56,8,2}*1792a, {56,8,2}*1792b, {56,8,2}*1792c, {56,8,2}*1792d, {56,2,8}*1792, {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, {28,16,2}*1792a, {112,4,2}*1792a, {28,16,2}*1792b, {112,4,2}*1792b, {28,4,2}*1792, {56,4,2}*1792b, {28,8,2}*1792b, {28,2,16}*1792, {112,2,4}*1792, {224,2,2}*1792
Permutation Representation (GAP) :
```s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)(21,22)
(23,26)(24,25)(27,28);;
s1 := ( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)(16,19)
(18,27)(20,24)(22,25)(26,28);;
s2 := (29,30);;
s3 := (31,32);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(32)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12)(13,14)(15,18)(16,17)(19,20)
(21,22)(23,26)(24,25)(27,28);
s1 := Sym(32)!( 1, 7)( 2, 4)( 3,13)( 5,15)( 6, 9)( 8,11)(10,21)(12,23)(14,17)
(16,19)(18,27)(20,24)(22,25)(26,28);
s2 := Sym(32)!(29,30);
s3 := Sym(32)!(31,32);
poly := sub<Sym(32)|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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```

to this polytope