Questions?
See the FAQ
or other info.

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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,2,4}*192
if this polytope has a name.
Group : SmallGroup(192,1472)
Rank : 5
Schlafli Type : {4,3,2,4}
Number of vertices, edges, etc : 4, 6, 3, 4, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,2,4,2} of size 384
{4,3,2,4,3} of size 576
{4,3,2,4,4} of size 768
{4,3,2,4,6} of size 1152
{4,3,2,4,3} of size 1152
{4,3,2,4,6} of size 1152
{4,3,2,4,6} of size 1152
{4,3,2,4,9} of size 1728
{4,3,2,4,4} of size 1728
{4,3,2,4,6} of size 1728
{4,3,2,4,10} of size 1920
Vertex Figure Of :
{2,4,3,2,4} of size 384
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,3,2,8}*384, {4,3,2,4}*384, {4,6,2,4}*384b, {4,6,2,4}*384c
3-fold covers : {4,9,2,4}*576, {4,3,2,12}*576, {4,3,6,4}*576
4-fold covers : {4,3,2,16}*768, {4,6,4,4}*768b, {4,12,2,4}*768b, {4,12,2,4}*768c, {4,3,2,8}*768, {4,6,2,8}*768b, {4,6,2,8}*768c, {8,3,2,4}*768, {4,6,2,4}*768, {4,3,4,4}*768b
5-fold covers : {4,3,2,20}*960, {4,15,2,4}*960
6-fold covers : {4,9,2,8}*1152, {4,9,2,4}*1152, {4,18,2,4}*1152b, {4,18,2,4}*1152c, {4,3,2,24}*1152, {4,3,6,8}*1152, {4,3,2,12}*1152, {4,6,2,12}*1152b, {4,6,2,12}*1152c, {4,6,6,4}*1152e, {12,3,2,4}*1152, {12,6,2,4}*1152d, {4,3,6,4}*1152, {4,6,6,4}*1152f, {4,6,6,4}*1152i
7-fold covers : {4,3,2,28}*1344, {4,21,2,4}*1344
9-fold covers : {4,27,2,4}*1728, {4,3,2,36}*1728, {4,9,2,12}*1728, {4,3,6,12}*1728a, {4,9,6,4}*1728, {4,3,6,4}*1728a, {4,3,6,12}*1728b, {4,3,6,4}*1728b
10-fold covers : {4,3,2,40}*1920, {4,15,2,8}*1920, {4,3,2,20}*1920, {4,6,2,20}*1920b, {4,6,2,20}*1920c, {4,6,10,4}*1920b, {20,6,2,4}*1920b, {4,15,2,4}*1920, {4,30,2,4}*1920b, {4,30,2,4}*1920c
Permutation Representation (GAP) :
```s0 := (1,2)(3,4);;
s1 := (2,3);;
s2 := (3,4);;
s3 := (6,7);;
s4 := (5,6)(7,8);;
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, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope