# Polytope of Type {21,4,2}

Atlas Canonical Name : {21,4,2}*336
if this polytope has a name.
Group : SmallGroup(336,215)
Rank : 4
Schlafli Type : {21,4,2}
Number of vertices, edges, etc : 21, 42, 4, 2
Order of s0s1s2s3 : 42
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{21,4,2,2} of size 672
{21,4,2,3} of size 1008
{21,4,2,4} of size 1344
{21,4,2,5} of size 1680
Vertex Figure Of :
{2,21,4,2} of size 672
{4,21,4,2} of size 1344
Quotients (Maximal Quotients in Boldface) :
7-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {21,4,2}*672, {42,4,2}*672b, {42,4,2}*672c
3-fold covers : {63,4,2}*1008
4-fold covers : {21,4,4}*1344a, {84,4,2}*1344b, {84,4,2}*1344c, {21,4,4}*1344b, {21,8,2}*1344, {42,4,2}*1344
5-fold covers : {105,4,2}*1680
Permutation Representation (GAP) :
```s0 := ( 3, 4)( 5,25)( 6,26)( 7,28)( 8,27)( 9,21)(10,22)(11,24)(12,23)(13,17)
(14,18)(15,20)(16,19);;
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 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
(21,22)(23,24)(25,26)(27,28);;
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,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s2*s1*s2*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(30)!( 3, 4)( 5,25)( 6,26)( 7,28)( 8,27)( 9,21)(10,22)(11,24)(12,23)
(13,17)(14,18)(15,20)(16,19);
s1 := Sym(30)!( 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(30)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)
(19,20)(21,22)(23,24)(25,26)(27,28);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s1*s0*s2*s1*s2*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