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

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

```

to this polytope