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

Atlas Canonical Name : {2,4,3,2}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 5
Schlafli Type : {2,4,3,2}
Number of vertices, edges, etc : 2, 4, 6, 3, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,3,2,2} of size 192
{2,4,3,2,3} of size 288
{2,4,3,2,4} of size 384
{2,4,3,2,5} of size 480
{2,4,3,2,6} of size 576
{2,4,3,2,7} of size 672
{2,4,3,2,8} of size 768
{2,4,3,2,9} of size 864
{2,4,3,2,10} of size 960
{2,4,3,2,11} of size 1056
{2,4,3,2,12} of size 1152
{2,4,3,2,13} of size 1248
{2,4,3,2,14} of size 1344
{2,4,3,2,15} of size 1440
{2,4,3,2,17} of size 1632
{2,4,3,2,18} of size 1728
{2,4,3,2,19} of size 1824
{2,4,3,2,20} of size 1920
Vertex Figure Of :
{2,2,4,3,2} of size 192
{3,2,4,3,2} of size 288
{4,2,4,3,2} of size 384
{5,2,4,3,2} of size 480
{6,2,4,3,2} of size 576
{7,2,4,3,2} of size 672
{8,2,4,3,2} of size 768
{9,2,4,3,2} of size 864
{10,2,4,3,2} of size 960
{11,2,4,3,2} of size 1056
{12,2,4,3,2} of size 1152
{13,2,4,3,2} of size 1248
{14,2,4,3,2} of size 1344
{15,2,4,3,2} of size 1440
{17,2,4,3,2} of size 1632
{18,2,4,3,2} of size 1728
{19,2,4,3,2} of size 1824
{20,2,4,3,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,3,2}*192, {2,4,6,2}*192b, {2,4,6,2}*192c
3-fold covers : {2,4,9,2}*288, {2,4,3,6}*288
4-fold covers : {4,4,3,2}*384a, {2,4,12,2}*384b, {2,4,12,2}*384c, {2,4,6,4}*384c, {4,4,3,2}*384b, {2,8,3,2}*384, {2,4,6,2}*384, {2,4,3,4}*384a
5-fold covers : {2,4,15,2}*480
6-fold covers : {2,4,9,2}*576, {2,4,18,2}*576b, {2,4,18,2}*576c, {2,4,3,6}*576, {2,4,6,6}*576d, {2,4,6,6}*576e, {2,4,6,6}*576f, {2,12,3,2}*576, {2,12,6,2}*576d, {6,4,3,2}*576
7-fold covers : {2,4,21,2}*672
8-fold covers : {4,4,3,2}*768a, {2,4,12,4}*768d, {2,4,12,4}*768e, {2,8,3,2}*768, {2,8,6,2}*768a, {2,4,6,2}*768a, {4,4,3,2}*768b, {4,4,6,2}*768b, {4,4,6,2}*768c, {2,4,24,2}*768c, {2,4,24,2}*768d, {4,8,3,2}*768, {2,4,6,8}*768b, {8,4,3,2}*768, {2,4,12,2}*768b, {2,4,6,2}*768b, {2,4,6,4}*768b, {2,4,12,2}*768c, {4,4,6,2}*768d, {2,8,6,2}*768b, {2,8,6,2}*768c, {2,4,3,8}*768, {2,4,3,4}*768, {2,4,6,4}*768c, {2,4,6,4}*768f
9-fold covers : {2,4,27,2}*864, {2,4,9,6}*864, {2,4,3,6}*864
10-fold covers : {2,4,6,10}*960b, {2,20,6,2}*960b, {10,4,3,2}*960, {2,4,15,2}*960, {2,4,30,2}*960b, {2,4,30,2}*960c
11-fold covers : {2,4,33,2}*1056
12-fold covers : {4,4,9,2}*1152a, {2,4,36,2}*1152b, {2,4,36,2}*1152c, {2,4,18,4}*1152c, {4,4,9,2}*1152b, {2,8,9,2}*1152, {4,4,3,6}*1152a, {2,4,18,2}*1152, {2,4,9,4}*1152a, {2,4,12,6}*1152d, {2,4,12,6}*1152e, {2,4,12,6}*1152f, {2,4,12,6}*1152g, {2,4,6,12}*1152d, {12,4,3,2}*1152, {4,4,3,6}*1152b, {2,24,3,2}*1152, {2,8,3,6}*1152, {6,8,3,2}*1152, {2,4,6,12}*1152e, {4,12,3,2}*1152, {2,4,3,6}*1152, {2,4,6,6}*1152a, {2,4,6,6}*1152b, {2,12,6,2}*1152a, {2,12,6,2}*1152b, {6,4,6,2}*1152a, {2,4,3,12}*1152
13-fold covers : {2,4,39,2}*1248
14-fold covers : {2,4,6,14}*1344b, {2,28,6,2}*1344b, {14,4,3,2}*1344, {2,4,21,2}*1344, {2,4,42,2}*1344b, {2,4,42,2}*1344c
15-fold covers : {2,4,45,2}*1440, {2,4,15,6}*1440
17-fold covers : {2,4,51,2}*1632
18-fold covers : {2,4,27,2}*1728, {2,4,54,2}*1728b, {2,4,54,2}*1728c, {2,4,6,18}*1728c, {2,36,6,2}*1728c, {18,4,3,2}*1728, {2,4,9,6}*1728, {2,4,18,6}*1728c, {2,4,18,6}*1728d, {2,4,18,6}*1728e, {2,12,9,2}*1728, {2,12,18,2}*1728c, {6,4,9,2}*1728, {2,4,3,6}*1728, {2,4,6,6}*1728d, {2,4,6,6}*1728e, {2,4,6,6}*1728f, {2,12,3,2}*1728, {2,12,6,2}*1728d, {6,12,3,2}*1728a, {6,4,3,6}*1728, {2,4,6,6}*1728i, {2,12,3,6}*1728, {2,12,6,6}*1728h, {6,12,3,2}*1728b, {6,12,6,2}*1728h
19-fold covers : {2,4,57,2}*1824
20-fold covers : {4,4,15,2}*1920a, {2,4,12,10}*1920b, {2,4,12,10}*1920c, {2,4,6,20}*1920b, {20,4,3,2}*1920, {10,8,3,2}*1920, {2,4,60,2}*1920b, {2,4,60,2}*1920c, {2,4,30,4}*1920c, {4,4,15,2}*1920b, {2,8,15,2}*1920, {2,4,6,10}*1920a, {2,20,6,2}*1920a, {10,4,6,2}*1920, {2,4,30,2}*1920, {2,4,15,4}*1920a
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4)(5,6);;
s2 := (4,5);;
s3 := (5,6);;
s4 := (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*s1*s0*s1,
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, s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope