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# Polytope of Type {4,2,4,3}

Atlas Canonical Name : {4,2,4,3}*384
if this polytope has a name.
Group : SmallGroup(384,20051)
Rank : 5
Schlafli Type : {4,2,4,3}
Number of vertices, edges, etc : 4, 4, 8, 12, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,2,4,3,2} of size 768
Vertex Figure Of :
{2,4,2,4,3} of size 768
{3,4,2,4,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,2,4,3}*192, {2,2,4,3}*192
4-fold quotients : {4,2,2,3}*96, {2,2,4,3}*96
8-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,4,3}*768b, {8,2,4,3}*768, {4,2,8,3}*768, {4,2,4,6}*768
3-fold covers : {4,2,4,9}*1152, {12,2,4,3}*1152, {4,6,4,3}*1152a, {4,2,12,3}*1152
5-fold covers : {20,2,4,3}*1920, {4,10,4,3}*1920, {4,2,4,15}*1920
Permutation Representation (GAP) :
```s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 8,10);;
s3 := ( 7, 8)( 9,10);;
s4 := (5,7)(6,9);;
poly := Group([s0,s1,s2,s3,s4]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(10)!(2,3);
s1 := Sym(10)!(1,2)(3,4);
s2 := Sym(10)!( 8,10);
s3 := Sym(10)!( 7, 8)( 9,10);
s4 := Sym(10)!(5,7)(6,9);
poly := sub<Sym(10)|s0,s1,s2,s3,s4>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope