Questions?
See the FAQ
or other info.

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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,4,2}*384a
if this polytope has a name.
Group : SmallGroup(384,17948)
Rank : 5
Schlafli Type : {3,4,4,2}
Number of vertices, edges, etc : 3, 12, 16, 8, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,4,4,2,2} of size 768
{3,4,4,2,3} of size 1152
{3,4,4,2,5} of size 1920
Vertex Figure Of :
{2,3,4,4,2} of size 768
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {3,4,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,4,4,4}*768a, {3,4,4,2}*768a, {3,4,4,2}*768b, {6,4,4,2}*768b, {6,4,4,2}*768c
3-fold covers : {9,4,4,2}*1152a, {3,4,4,6}*1152a
5-fold covers : {3,4,4,10}*1920a, {15,4,4,2}*1920a
Permutation Representation (GAP) :
```s0 := ( 1, 9)( 2,10)( 3,11)( 4,12);;
s1 := ( 5, 9)( 6,10)( 7,11)( 8,12);;
s2 := ( 1, 3)( 2, 4)( 9,11)(10,12);;
s3 := ( 3, 4)( 7, 8)(11,12);;
s4 := (13,14);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s2*s1*s0*s2*s1*s0*s2*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(14)!( 1, 9)( 2,10)( 3,11)( 4,12);
s1 := Sym(14)!( 5, 9)( 6,10)( 7,11)( 8,12);
s2 := Sym(14)!( 1, 3)( 2, 4)( 9,11)(10,12);
s3 := Sym(14)!( 3, 4)( 7, 8)(11,12);
s4 := Sym(14)!(13,14);
poly := sub<Sym(14)|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, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s2*s1*s0*s2*s1*s0*s2*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;

```

to this polytope