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Polytope of Type {28,6}

Atlas Canonical Name : {28,6}*336b
if this polytope has a name.
Group : SmallGroup(336,212)
Rank : 3
Schlafli Type : {28,6}
Number of vertices, edges, etc : 28, 84, 6
Order of s0s1s2 : 21
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{28,6,2} of size 672
{28,6,4} of size 1344
Vertex Figure Of :
{2,28,6} of size 672
Quotients (Maximal Quotients in Boldface) :
7-fold quotients : {4,6}*48b
14-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {28,6}*672
3-fold covers : {28,18}*1008b, {84,6}*1008d
4-fold covers : {56,6}*1344a, {28,12}*1344b, {28,6}*1344e, {56,6}*1344b, {56,6}*1344c, {28,12}*1344c
5-fold covers : {28,30}*1680b, {140,6}*1680b
Permutation Representation (GAP) :
```s0 := ( 1, 3)( 2, 4)( 5,27)( 6,28)( 7,25)( 8,26)( 9,23)(10,24)(11,21)(12,22)
(13,19)(14,20)(15,17)(16,18);;
s1 := ( 1, 5)( 2, 7)( 3, 6)( 4, 8)( 9,25)(10,27)(11,26)(12,28)(13,21)(14,23)
(15,22)(16,24)(18,19);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0 ];;
poly := F / rels;;

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

```
References : None.
to this polytope