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

Atlas Canonical Name : {4,3,2,3}*144
if this polytope has a name.
Group : SmallGroup(144,183)
Rank : 5
Schlafli Type : {4,3,2,3}
Number of vertices, edges, etc : 4, 6, 3, 3, 3
Order of s0s1s2s3s4 : 3
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,2,3,2} of size 288
{4,3,2,3,3} of size 576
{4,3,2,3,4} of size 576
{4,3,2,3,6} of size 864
{4,3,2,3,4} of size 1152
{4,3,2,3,6} of size 1152
{4,3,2,3,5} of size 1440
Vertex Figure Of :
{2,4,3,2,3} of size 288
{4,4,3,2,3} of size 1152
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,3,2,3}*288, {4,3,2,6}*288, {4,6,2,3}*288b, {4,6,2,3}*288c
3-fold covers : {4,3,2,9}*432, {4,9,2,3}*432, {4,3,6,3}*432
4-fold covers : {4,12,2,3}*576b, {4,12,2,3}*576c, {4,3,2,12}*576, {8,3,2,3}*576, {4,3,2,6}*576, {4,6,2,3}*576, {4,6,2,6}*576b, {4,6,2,6}*576c
5-fold covers : {4,15,2,3}*720, {4,3,2,15}*720
6-fold covers : {4,3,2,9}*864, {4,3,2,18}*864, {4,6,2,9}*864b, {4,6,2,9}*864c, {4,9,2,3}*864, {4,9,2,6}*864, {4,18,2,3}*864b, {4,18,2,3}*864c, {4,3,6,3}*864, {4,3,6,6}*864a, {4,6,6,3}*864b, {4,6,6,3}*864c, {4,3,6,6}*864b, {4,6,6,3}*864e, {12,3,2,3}*864, {12,6,2,3}*864d
7-fold covers : {4,21,2,3}*1008, {4,3,2,21}*1008
8-fold covers : {4,6,2,3}*1152a, {8,3,2,3}*1152, {8,6,2,3}*1152a, {4,24,2,3}*1152c, {4,24,2,3}*1152d, {4,3,2,24}*1152, {4,12,2,3}*1152b, {4,12,2,6}*1152b, {4,12,2,6}*1152c, {4,3,2,12}*1152, {4,6,2,12}*1152b, {4,6,2,12}*1152c, {4,6,4,6}*1152b, {4,6,2,3}*1152b, {4,12,2,3}*1152c, {8,3,2,6}*1152, {8,6,2,3}*1152b, {8,6,2,3}*1152c, {4,6,4,3}*1152b, {4,6,2,6}*1152, {4,3,4,6}*1152
9-fold covers : {4,3,2,27}*1296, {4,27,2,3}*1296, {4,9,2,9}*1296, {4,3,6,9}*1296, {4,3,6,3}*1296a, {4,9,6,3}*1296, {4,3,6,3}*1296b
10-fold covers : {20,6,2,3}*1440b, {4,15,2,3}*1440, {4,15,2,6}*1440, {4,30,2,3}*1440b, {4,30,2,3}*1440c, {4,3,2,15}*1440, {4,3,2,30}*1440, {4,6,2,15}*1440b, {4,6,2,15}*1440c
11-fold covers : {4,33,2,3}*1584, {4,3,2,33}*1584
12-fold covers : {4,12,2,9}*1728b, {4,12,2,9}*1728c, {4,3,2,36}*1728, {8,3,2,9}*1728, {4,36,2,3}*1728b, {4,36,2,3}*1728c, {4,9,2,12}*1728, {4,12,6,3}*1728b, {4,12,6,3}*1728c, {4,3,6,12}*1728a, {8,9,2,3}*1728, {8,3,6,3}*1728, {4,3,2,18}*1728, {4,6,2,9}*1728, {4,6,2,18}*1728b, {4,6,2,18}*1728c, {4,9,2,6}*1728, {4,18,2,3}*1728, {4,18,2,6}*1728b, {4,18,2,6}*1728c, {4,3,6,6}*1728a, {4,6,6,3}*1728a, {4,6,6,6}*1728b, {4,6,6,6}*1728c, {24,3,2,3}*1728, {4,12,6,3}*1728e, {4,12,6,3}*1728f, {4,3,6,12}*1728b, {4,3,6,6}*1728b, {4,6,6,3}*1728b, {4,6,6,6}*1728j, {4,6,6,6}*1728k, {4,6,6,6}*1728m, {4,6,6,6}*1728n, {12,3,2,6}*1728, {12,6,2,3}*1728a, {12,6,2,3}*1728b, {12,6,2,6}*1728d
13-fold covers : {4,39,2,3}*1872, {4,3,2,39}*1872
Permutation Representation (GAP) :
```s0 := (1,2)(3,4);;
s1 := (2,3);;
s2 := (3,4);;
s3 := (6,7);;
s4 := (5,6);;
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, s3*s4*s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope