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

Atlas Canonical Name : {2,4,2,3}*96
if this polytope has a name.
Group : SmallGroup(96,209)
Rank : 5
Schlafli Type : {2,4,2,3}
Number of vertices, edges, etc : 2, 4, 4, 3, 3
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,2,3,2} of size 192
{2,4,2,3,3} of size 384
{2,4,2,3,4} of size 384
{2,4,2,3,6} of size 576
{2,4,2,3,4} of size 768
{2,4,2,3,6} of size 768
{2,4,2,3,5} of size 960
{2,4,2,3,6} of size 1728
{2,4,2,3,5} of size 1920
{2,4,2,3,10} of size 1920
{2,4,2,3,10} of size 1920
Vertex Figure Of :
{2,2,4,2,3} of size 192
{3,2,4,2,3} of size 288
{4,2,4,2,3} of size 384
{5,2,4,2,3} of size 480
{6,2,4,2,3} of size 576
{7,2,4,2,3} of size 672
{8,2,4,2,3} of size 768
{9,2,4,2,3} of size 864
{10,2,4,2,3} of size 960
{11,2,4,2,3} of size 1056
{12,2,4,2,3} of size 1152
{13,2,4,2,3} of size 1248
{14,2,4,2,3} of size 1344
{15,2,4,2,3} of size 1440
{17,2,4,2,3} of size 1632
{18,2,4,2,3} of size 1728
{19,2,4,2,3} of size 1824
{20,2,4,2,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,2,3}*192, {2,8,2,3}*192, {2,4,2,6}*192
3-fold covers : {2,4,2,9}*288, {2,12,2,3}*288, {6,4,2,3}*288a, {2,4,6,3}*288
4-fold covers : {4,8,2,3}*384a, {8,4,2,3}*384a, {4,8,2,3}*384b, {8,4,2,3}*384b, {4,4,2,3}*384, {2,16,2,3}*384, {2,4,2,12}*384, {2,4,4,6}*384, {4,4,2,6}*384, {2,8,2,6}*384, {2,4,4,3}*384b
5-fold covers : {2,20,2,3}*480, {10,4,2,3}*480, {2,4,2,15}*480
6-fold covers : {4,4,2,9}*576, {2,8,2,9}*576, {2,4,2,18}*576, {4,12,2,3}*576a, {12,4,2,3}*576a, {2,24,2,3}*576, {6,8,2,3}*576, {2,8,6,3}*576, {4,4,6,3}*576, {2,12,2,6}*576, {2,4,6,6}*576a, {6,4,2,6}*576a, {2,4,6,6}*576c
7-fold covers : {2,28,2,3}*672, {14,4,2,3}*672, {2,4,2,21}*672
8-fold covers : {4,8,2,3}*768a, {8,4,2,3}*768a, {8,8,2,3}*768a, {8,8,2,3}*768b, {8,8,2,3}*768c, {8,8,2,3}*768d, {4,16,2,3}*768a, {16,4,2,3}*768a, {4,16,2,3}*768b, {16,4,2,3}*768b, {4,4,2,3}*768, {4,8,2,3}*768b, {8,4,2,3}*768b, {2,32,2,3}*768, {4,4,4,6}*768, {2,4,4,12}*768, {4,4,2,12}*768, {2,4,8,6}*768a, {2,8,4,6}*768a, {4,8,2,6}*768a, {8,4,2,6}*768a, {2,4,8,6}*768b, {2,8,4,6}*768b, {4,8,2,6}*768b, {8,4,2,6}*768b, {2,4,4,6}*768a, {4,4,2,6}*768, {2,8,2,12}*768, {2,4,2,24}*768, {2,16,2,6}*768, {4,4,4,3}*768b, {2,4,8,3}*768, {2,8,4,3}*768, {2,4,4,6}*768d
9-fold covers : {2,4,2,27}*864, {2,36,2,3}*864, {2,12,2,9}*864, {2,12,6,3}*864a, {6,4,2,9}*864a, {18,4,2,3}*864a, {2,4,6,9}*864, {2,4,6,3}*864a, {6,12,2,3}*864a, {6,12,2,3}*864b, {2,12,6,3}*864b, {6,4,6,3}*864, {6,12,2,3}*864c, {2,4,6,3}*864b, {6,4,2,3}*864
10-fold covers : {4,20,2,3}*960, {20,4,2,3}*960, {2,40,2,3}*960, {10,8,2,3}*960, {4,4,2,15}*960, {2,8,2,15}*960, {2,20,2,6}*960, {2,4,10,6}*960, {10,4,2,6}*960, {2,4,2,30}*960
11-fold covers : {2,44,2,3}*1056, {22,4,2,3}*1056, {2,4,2,33}*1056
12-fold covers : {4,8,2,9}*1152a, {8,4,2,9}*1152a, {8,4,6,3}*1152a, {8,12,2,3}*1152a, {12,8,2,3}*1152a, {4,8,6,3}*1152a, {4,24,2,3}*1152a, {24,4,2,3}*1152a, {4,8,2,9}*1152b, {8,4,2,9}*1152b, {8,4,6,3}*1152b, {8,12,2,3}*1152b, {12,8,2,3}*1152b, {4,8,6,3}*1152b, {4,24,2,3}*1152b, {24,4,2,3}*1152b, {4,4,2,9}*1152, {4,4,6,3}*1152, {4,12,2,3}*1152a, {12,4,2,3}*1152a, {2,16,2,9}*1152, {6,16,2,3}*1152, {2,16,6,3}*1152, {2,48,2,3}*1152, {2,4,4,18}*1152, {4,4,2,18}*1152, {4,4,6,6}*1152a, {6,4,4,6}*1152, {4,4,6,6}*1152c, {2,4,12,6}*1152a, {2,12,4,6}*1152, {4,12,2,6}*1152a, {12,4,2,6}*1152a, {2,4,12,6}*1152c, {2,4,2,36}*1152, {6,4,2,12}*1152a, {2,4,6,12}*1152b, {2,4,6,12}*1152c, {2,12,2,12}*1152, {2,8,2,18}*1152, {2,8,6,6}*1152a, {6,8,2,6}*1152, {2,8,6,6}*1152c, {2,24,2,6}*1152, {2,4,4,9}*1152b, {4,12,2,3}*1152b, {2,12,4,3}*1152, {6,4,4,3}*1152b, {6,4,2,3}*1152b, {6,12,2,3}*1152a, {2,4,6,3}*1152a, {2,4,12,3}*1152
13-fold covers : {2,52,2,3}*1248, {26,4,2,3}*1248, {2,4,2,39}*1248
14-fold covers : {4,28,2,3}*1344, {28,4,2,3}*1344, {2,56,2,3}*1344, {14,8,2,3}*1344, {4,4,2,21}*1344, {2,8,2,21}*1344, {2,28,2,6}*1344, {2,4,14,6}*1344, {14,4,2,6}*1344, {2,4,2,42}*1344
15-fold covers : {2,20,2,9}*1440, {10,4,2,9}*1440, {2,4,2,45}*1440, {10,12,2,3}*1440, {6,20,2,3}*1440a, {2,20,6,3}*1440, {10,4,6,3}*1440, {2,12,2,15}*1440, {2,60,2,3}*1440, {6,4,2,15}*1440a, {30,4,2,3}*1440a, {2,4,6,15}*1440
17-fold covers : {2,68,2,3}*1632, {34,4,2,3}*1632, {2,4,2,51}*1632
18-fold covers : {4,4,2,27}*1728, {2,8,2,27}*1728, {2,4,2,54}*1728, {4,12,2,9}*1728a, {12,4,2,9}*1728a, {4,36,2,3}*1728a, {36,4,2,3}*1728a, {4,12,6,3}*1728a, {2,72,2,3}*1728, {2,24,2,9}*1728, {2,24,6,3}*1728a, {6,8,2,9}*1728, {18,8,2,3}*1728, {2,8,6,9}*1728, {4,4,6,9}*1728, {2,8,6,3}*1728a, {4,4,6,3}*1728a, {2,12,2,18}*1728, {2,36,2,6}*1728, {2,12,6,6}*1728a, {2,4,6,18}*1728a, {2,4,18,6}*1728a, {6,4,2,18}*1728a, {18,4,2,6}*1728a, {2,4,6,6}*1728b, {2,4,6,18}*1728b, {2,4,6,6}*1728c, {6,24,2,3}*1728a, {6,24,2,3}*1728b, {2,24,6,3}*1728b, {12,12,2,3}*1728a, {12,12,2,3}*1728b, {12,12,2,3}*1728c, {12,4,6,3}*1728, {6,8,6,3}*1728, {6,24,2,3}*1728c, {4,12,6,3}*1728d, {6,8,2,3}*1728, {2,8,6,3}*1728b, {4,4,6,3}*1728b, {4,4,2,3}*1728, {4,12,2,3}*1728, {12,4,2,3}*1728, {2,12,6,6}*1728b, {2,12,6,6}*1728d, {6,12,2,6}*1728a, {6,12,2,6}*1728b, {6,4,6,6}*1728a, {2,12,6,6}*1728e, {6,4,6,6}*1728c, {2,4,6,6}*1728h, {2,12,6,6}*1728f, {6,12,2,6}*1728c, {2,4,6,6}*1728j, {2,4,6,6}*1728k, {6,4,2,6}*1728
19-fold covers : {2,76,2,3}*1824, {38,4,2,3}*1824, {2,4,2,57}*1824
20-fold covers : {4,8,2,15}*1920a, {8,4,2,15}*1920a, {8,20,2,3}*1920a, {20,8,2,3}*1920a, {4,40,2,3}*1920a, {40,4,2,3}*1920a, {4,8,2,15}*1920b, {8,4,2,15}*1920b, {8,20,2,3}*1920b, {20,8,2,3}*1920b, {4,40,2,3}*1920b, {40,4,2,3}*1920b, {4,4,2,15}*1920, {4,20,2,3}*1920, {20,4,2,3}*1920, {2,16,2,15}*1920, {10,16,2,3}*1920, {2,80,2,3}*1920, {2,4,4,30}*1920, {4,4,2,30}*1920, {4,4,10,6}*1920, {10,4,4,6}*1920, {2,4,20,6}*1920, {2,20,4,6}*1920, {4,20,2,6}*1920, {20,4,2,6}*1920, {2,4,2,60}*1920, {10,4,2,12}*1920, {2,4,10,12}*1920, {2,20,2,12}*1920, {2,8,2,30}*1920, {2,8,10,6}*1920, {10,8,2,6}*1920, {2,40,2,6}*1920, {2,20,4,3}*1920, {10,4,4,3}*1920b, {2,4,4,15}*1920b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4)(5,6);;
s3 := (8,9);;
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,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope