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

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

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

```

to this polytope