Questions?
See the FAQ
or other info.

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

Atlas Canonical Name : {2,3,2,4}*96
if this polytope has a name.
Group : SmallGroup(96,209)
Rank : 5
Schlafli Type : {2,3,2,4}
Number of vertices, edges, etc : 2, 3, 3, 4, 4
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,3,2,4,2} of size 192
{2,3,2,4,3} of size 288
{2,3,2,4,4} of size 384
{2,3,2,4,6} of size 576
{2,3,2,4,3} of size 576
{2,3,2,4,6} of size 576
{2,3,2,4,6} of size 576
{2,3,2,4,8} of size 768
{2,3,2,4,8} of size 768
{2,3,2,4,4} of size 768
{2,3,2,4,9} of size 864
{2,3,2,4,4} of size 864
{2,3,2,4,6} of size 864
{2,3,2,4,10} of size 960
{2,3,2,4,12} of size 1152
{2,3,2,4,12} of size 1152
{2,3,2,4,12} of size 1152
{2,3,2,4,6} of size 1152
{2,3,2,4,14} of size 1344
{2,3,2,4,5} of size 1440
{2,3,2,4,6} of size 1440
{2,3,2,4,15} of size 1440
{2,3,2,4,18} of size 1728
{2,3,2,4,9} of size 1728
{2,3,2,4,18} of size 1728
{2,3,2,4,18} of size 1728
{2,3,2,4,4} of size 1728
{2,3,2,4,6} of size 1728
{2,3,2,4,20} of size 1920
{2,3,2,4,5} of size 1920
Vertex Figure Of :
{2,2,3,2,4} of size 192
{3,2,3,2,4} of size 288
{4,2,3,2,4} of size 384
{5,2,3,2,4} of size 480
{6,2,3,2,4} of size 576
{7,2,3,2,4} of size 672
{8,2,3,2,4} of size 768
{9,2,3,2,4} of size 864
{10,2,3,2,4} of size 960
{11,2,3,2,4} of size 1056
{12,2,3,2,4} of size 1152
{13,2,3,2,4} of size 1248
{14,2,3,2,4} of size 1344
{15,2,3,2,4} of size 1440
{17,2,3,2,4} of size 1632
{18,2,3,2,4} of size 1728
{19,2,3,2,4} of size 1824
{20,2,3,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,3,2,8}*192, {2,6,2,4}*192
3-fold covers : {2,9,2,4}*288, {2,3,2,12}*288, {6,3,2,4}*288, {2,3,6,4}*288
4-fold covers : {2,3,2,16}*384, {2,12,2,4}*384, {2,6,4,4}*384, {4,6,2,4}*384a, {2,6,2,8}*384, {2,3,4,4}*384b, {4,3,2,4}*384
5-fold covers : {2,3,2,20}*480, {2,15,2,4}*480
6-fold covers : {2,9,2,8}*576, {2,18,2,4}*576, {2,3,2,24}*576, {6,3,2,8}*576, {2,3,6,8}*576, {2,6,2,12}*576, {2,6,6,4}*576a, {6,6,2,4}*576a, {6,6,2,4}*576b, {2,6,6,4}*576c
7-fold covers : {2,3,2,28}*672, {2,21,2,4}*672
8-fold covers : {2,3,2,32}*768, {2,12,4,4}*768, {4,6,4,4}*768a, {4,12,2,4}*768a, {2,6,4,8}*768a, {2,6,8,4}*768a, {2,6,4,8}*768b, {2,6,8,4}*768b, {2,6,4,4}*768a, {4,6,2,8}*768a, {8,6,2,4}*768, {2,12,2,8}*768, {2,24,2,4}*768, {2,6,2,16}*768, {2,3,8,4}*768, {2,3,4,8}*768, {4,3,2,8}*768, {8,3,2,4}*768, {2,6,4,4}*768d, {4,6,2,4}*768
9-fold covers : {2,27,2,4}*864, {2,3,2,36}*864, {2,9,2,12}*864, {2,3,6,12}*864a, {6,9,2,4}*864, {6,3,2,4}*864, {2,9,6,4}*864, {2,3,6,4}*864a, {6,3,2,12}*864, {2,3,6,12}*864b, {6,3,6,4}*864, {2,3,6,4}*864b
10-fold covers : {2,3,2,40}*960, {2,15,2,8}*960, {2,6,2,20}*960, {2,6,10,4}*960, {10,6,2,4}*960, {2,30,2,4}*960
11-fold covers : {2,3,2,44}*1056, {2,33,2,4}*1056
12-fold covers : {2,9,2,16}*1152, {6,3,2,16}*1152, {2,3,6,16}*1152, {2,3,2,48}*1152, {2,18,4,4}*1152, {6,6,4,4}*1152a, {6,6,4,4}*1152b, {2,6,4,12}*1152, {2,6,12,4}*1152a, {2,6,12,4}*1152c, {4,18,2,4}*1152a, {2,36,2,4}*1152, {4,6,6,4}*1152a, {4,6,6,4}*1152b, {12,6,2,4}*1152a, {4,6,2,12}*1152a, {6,12,2,4}*1152b, {6,12,2,4}*1152c, {12,6,2,4}*1152b, {2,12,6,4}*1152b, {2,12,6,4}*1152c, {2,12,2,12}*1152, {2,18,2,8}*1152, {2,6,6,8}*1152a, {6,6,2,8}*1152a, {6,6,2,8}*1152b, {2,6,6,8}*1152c, {2,6,2,24}*1152, {2,9,4,4}*1152b, {4,9,2,4}*1152, {2,3,4,12}*1152, {4,3,2,12}*1152, {6,3,4,4}*1152b, {6,3,2,4}*1152, {12,3,2,4}*1152, {4,3,6,4}*1152, {2,3,6,4}*1152a, {2,3,12,4}*1152
13-fold covers : {2,3,2,52}*1248, {2,39,2,4}*1248
14-fold covers : {2,3,2,56}*1344, {2,21,2,8}*1344, {2,6,2,28}*1344, {2,6,14,4}*1344, {14,6,2,4}*1344, {2,42,2,4}*1344
15-fold covers : {2,9,2,20}*1440, {2,45,2,4}*1440, {6,3,2,20}*1440, {2,3,6,20}*1440, {2,15,2,12}*1440, {2,3,2,60}*1440, {6,15,2,4}*1440, {2,15,6,4}*1440
17-fold covers : {2,3,2,68}*1632, {2,51,2,4}*1632
18-fold covers : {2,27,2,8}*1728, {2,54,2,4}*1728, {2,3,2,72}*1728, {2,9,2,24}*1728, {2,3,6,24}*1728a, {6,9,2,8}*1728, {6,3,2,8}*1728, {2,9,6,8}*1728, {2,3,6,8}*1728a, {2,18,2,12}*1728, {2,6,2,36}*1728, {2,6,6,12}*1728a, {2,6,18,4}*1728a, {2,18,6,4}*1728a, {6,18,2,4}*1728a, {6,18,2,4}*1728b, {18,6,2,4}*1728a, {2,6,6,4}*1728b, {6,6,2,4}*1728a, {6,6,2,4}*1728b, {2,18,6,4}*1728b, {2,6,6,4}*1728c, {6,3,2,24}*1728, {2,3,6,24}*1728b, {6,3,6,8}*1728, {2,3,6,8}*1728b, {2,6,6,12}*1728b, {2,6,6,12}*1728c, {6,6,2,12}*1728a, {6,6,2,12}*1728b, {6,6,6,4}*1728d, {6,6,6,4}*1728f, {6,6,2,4}*1728d, {2,6,6,12}*1728e, {6,6,6,4}*1728g, {6,6,6,4}*1728h, {2,6,6,4}*1728h, {2,6,6,12}*1728f, {2,6,6,4}*1728j, {2,6,6,4}*1728k
19-fold covers : {2,3,2,76}*1824, {2,57,2,4}*1824
20-fold covers : {2,15,2,16}*1920, {2,3,2,80}*1920, {2,30,4,4}*1920, {10,6,4,4}*1920, {2,6,4,20}*1920, {2,6,20,4}*1920, {4,30,2,4}*1920a, {2,60,2,4}*1920, {4,6,10,4}*1920a, {10,12,2,4}*1920, {4,6,2,20}*1920a, {20,6,2,4}*1920a, {2,12,10,4}*1920, {2,12,2,20}*1920, {2,30,2,8}*1920, {2,6,10,8}*1920, {10,6,2,8}*1920, {2,6,2,40}*1920, {2,3,4,20}*1920, {4,3,2,20}*1920, {2,15,4,4}*1920b, {4,15,2,4}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := (7,8);;
s4 := (6,7)(8,9);;
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*s1*s0*s1,
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*s3*s4 ];;
poly := F / rels;;

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

```

to this polytope