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

Atlas Canonical Name : {2,3,2,2,2}*96
if this polytope has a name.
Group : SmallGroup(96,230)
Rank : 6
Schlafli Type : {2,3,2,2,2}
Number of vertices, edges, etc : 2, 3, 3, 2, 2, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,3,2,2,2,2} of size 192
{2,3,2,2,2,3} of size 288
{2,3,2,2,2,4} of size 384
{2,3,2,2,2,5} of size 480
{2,3,2,2,2,6} of size 576
{2,3,2,2,2,7} of size 672
{2,3,2,2,2,8} of size 768
{2,3,2,2,2,9} of size 864
{2,3,2,2,2,10} of size 960
{2,3,2,2,2,11} of size 1056
{2,3,2,2,2,12} of size 1152
{2,3,2,2,2,13} of size 1248
{2,3,2,2,2,14} of size 1344
{2,3,2,2,2,15} of size 1440
{2,3,2,2,2,17} of size 1632
{2,3,2,2,2,18} of size 1728
{2,3,2,2,2,19} of size 1824
{2,3,2,2,2,20} of size 1920
Vertex Figure Of :
{2,2,3,2,2,2} of size 192
{3,2,3,2,2,2} of size 288
{4,2,3,2,2,2} of size 384
{5,2,3,2,2,2} of size 480
{6,2,3,2,2,2} of size 576
{7,2,3,2,2,2} of size 672
{8,2,3,2,2,2} of size 768
{9,2,3,2,2,2} of size 864
{10,2,3,2,2,2} of size 960
{11,2,3,2,2,2} of size 1056
{12,2,3,2,2,2} of size 1152
{13,2,3,2,2,2} of size 1248
{14,2,3,2,2,2} of size 1344
{15,2,3,2,2,2} of size 1440
{17,2,3,2,2,2} of size 1632
{18,2,3,2,2,2} of size 1728
{19,2,3,2,2,2} of size 1824
{20,2,3,2,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,3,2,2,4}*192, {2,3,2,4,2}*192, {2,6,2,2,2}*192
3-fold covers : {2,9,2,2,2}*288, {2,3,2,2,6}*288, {2,3,2,6,2}*288, {2,3,6,2,2}*288, {6,3,2,2,2}*288
4-fold covers : {2,3,2,4,4}*384, {2,3,2,2,8}*384, {2,3,2,8,2}*384, {2,12,2,2,2}*384, {2,6,2,2,4}*384, {2,6,2,4,2}*384, {2,6,4,2,2}*384a, {4,6,2,2,2}*384a, {2,3,4,2,2}*384, {4,3,2,2,2}*384
5-fold covers : {2,3,2,2,10}*480, {2,3,2,10,2}*480, {2,15,2,2,2}*480
6-fold covers : {2,9,2,2,4}*576, {2,9,2,4,2}*576, {2,18,2,2,2}*576, {2,3,2,2,12}*576, {2,3,2,12,2}*576, {2,3,2,4,6}*576a, {2,3,2,6,4}*576a, {2,3,6,2,4}*576, {6,3,2,2,4}*576, {6,3,2,4,2}*576, {2,3,6,4,2}*576, {2,6,2,2,6}*576, {2,6,2,6,2}*576, {2,6,6,2,2}*576a, {2,6,6,2,2}*576c, {6,6,2,2,2}*576a, {6,6,2,2,2}*576b
7-fold covers : {2,3,2,2,14}*672, {2,3,2,14,2}*672, {2,21,2,2,2}*672
8-fold covers : {2,3,2,4,8}*768a, {2,3,2,8,4}*768a, {2,3,2,4,8}*768b, {2,3,2,8,4}*768b, {2,3,2,4,4}*768, {2,3,2,2,16}*768, {2,3,2,16,2}*768, {2,6,2,4,4}*768, {2,6,4,4,2}*768, {2,12,4,2,2}*768a, {4,12,2,2,2}*768a, {2,6,4,2,4}*768a, {4,6,2,2,4}*768a, {4,6,2,4,2}*768a, {4,6,4,2,2}*768a, {2,12,2,2,4}*768, {2,12,2,4,2}*768, {2,6,2,2,8}*768, {2,6,2,8,2}*768, {2,6,8,2,2}*768, {8,6,2,2,2}*768, {2,24,2,2,2}*768, {2,3,4,2,4}*768, {2,3,4,4,2}*768b, {4,3,2,2,4}*768, {4,3,2,4,2}*768, {2,3,8,2,2}*768, {8,3,2,2,2}*768, {2,6,4,2,2}*768, {4,6,2,2,2}*768
9-fold covers : {2,27,2,2,2}*864, {2,3,2,2,18}*864, {2,3,2,18,2}*864, {2,9,2,2,6}*864, {2,9,2,6,2}*864, {2,9,6,2,2}*864, {6,9,2,2,2}*864, {2,3,6,2,2}*864, {2,3,6,6,2}*864a, {6,3,2,2,2}*864, {2,3,2,6,6}*864a, {2,3,2,6,6}*864b, {2,3,2,6,6}*864c, {2,3,6,2,6}*864, {2,3,6,6,2}*864b, {6,3,2,2,6}*864, {6,3,2,6,2}*864, {6,3,6,2,2}*864
10-fold covers : {2,3,2,2,20}*960, {2,3,2,20,2}*960, {2,3,2,4,10}*960, {2,3,2,10,4}*960, {2,15,2,2,4}*960, {2,15,2,4,2}*960, {2,6,2,2,10}*960, {2,6,2,10,2}*960, {2,6,10,2,2}*960, {10,6,2,2,2}*960, {2,30,2,2,2}*960
11-fold covers : {2,3,2,2,22}*1056, {2,3,2,22,2}*1056, {2,33,2,2,2}*1056
12-fold covers : {2,9,2,4,4}*1152, {6,3,2,4,4}*1152, {2,3,6,4,4}*1152, {2,3,2,4,12}*1152a, {2,3,2,12,4}*1152a, {2,9,2,2,8}*1152, {2,9,2,8,2}*1152, {2,3,2,6,8}*1152, {2,3,2,8,6}*1152, {2,3,6,2,8}*1152, {6,3,2,2,8}*1152, {6,3,2,8,2}*1152, {2,3,6,8,2}*1152, {2,3,2,2,24}*1152, {2,3,2,24,2}*1152, {2,18,2,2,4}*1152, {2,18,2,4,2}*1152, {2,18,4,2,2}*1152a, {4,18,2,2,2}*1152a, {2,36,2,2,2}*1152, {2,6,2,4,6}*1152a, {2,6,2,6,4}*1152a, {2,6,4,2,6}*1152a, {2,6,4,6,2}*1152, {2,6,6,2,4}*1152a, {2,6,6,2,4}*1152c, {2,6,6,4,2}*1152a, {4,6,2,2,6}*1152a, {4,6,2,6,2}*1152a, {4,6,6,2,2}*1152a, {4,6,6,2,2}*1152b, {6,6,2,2,4}*1152a, {6,6,2,2,4}*1152b, {6,6,2,4,2}*1152a, {6,6,2,4,2}*1152b, {6,6,4,2,2}*1152a, {6,6,4,2,2}*1152b, {2,6,6,4,2}*1152c, {2,6,12,2,2}*1152a, {12,6,2,2,2}*1152a, {2,6,2,2,12}*1152, {2,6,2,12,2}*1152, {2,6,12,2,2}*1152b, {2,12,2,2,6}*1152, {2,12,2,6,2}*1152, {2,12,6,2,2}*1152b, {2,12,6,2,2}*1152c, {6,12,2,2,2}*1152b, {6,12,2,2,2}*1152c, {12,6,2,2,2}*1152b, {2,9,4,2,2}*1152, {4,9,2,2,2}*1152, {2,3,2,4,6}*1152, {2,3,2,6,4}*1152, {2,3,2,6,6}*1152, {2,3,4,2,6}*1152, {2,3,4,6,2}*1152, {2,3,6,2,2}*1152, {2,3,12,2,2}*1152, {4,3,2,2,6}*1152, {4,3,2,6,2}*1152, {4,3,6,2,2}*1152, {6,3,2,2,2}*1152, {6,3,4,2,2}*1152, {12,3,2,2,2}*1152
13-fold covers : {2,3,2,2,26}*1248, {2,3,2,26,2}*1248, {2,39,2,2,2}*1248
14-fold covers : {2,3,2,2,28}*1344, {2,3,2,28,2}*1344, {2,3,2,4,14}*1344, {2,3,2,14,4}*1344, {2,21,2,2,4}*1344, {2,21,2,4,2}*1344, {2,6,2,2,14}*1344, {2,6,2,14,2}*1344, {2,6,14,2,2}*1344, {14,6,2,2,2}*1344, {2,42,2,2,2}*1344
15-fold covers : {2,9,2,2,10}*1440, {2,9,2,10,2}*1440, {2,45,2,2,2}*1440, {2,3,2,6,10}*1440, {2,3,2,10,6}*1440, {2,3,6,2,10}*1440, {2,3,6,10,2}*1440, {6,3,2,2,10}*1440, {6,3,2,10,2}*1440, {2,3,2,2,30}*1440, {2,3,2,30,2}*1440, {2,15,2,2,6}*1440, {2,15,2,6,2}*1440, {2,15,6,2,2}*1440, {6,15,2,2,2}*1440
17-fold covers : {2,3,2,2,34}*1632, {2,3,2,34,2}*1632, {2,51,2,2,2}*1632
18-fold covers : {2,27,2,2,4}*1728, {2,27,2,4,2}*1728, {2,54,2,2,2}*1728, {2,9,2,2,12}*1728, {2,9,2,12,2}*1728, {2,3,2,2,36}*1728, {2,3,2,36,2}*1728, {2,3,6,12,2}*1728a, {2,3,2,4,18}*1728a, {2,3,2,18,4}*1728a, {2,9,2,4,6}*1728a, {2,9,2,6,4}*1728a, {2,9,6,2,4}*1728, {6,9,2,2,4}*1728, {6,9,2,4,2}*1728, {2,3,6,2,4}*1728, {2,3,6,6,4}*1728a, {6,3,2,2,4}*1728, {6,3,2,4,2}*1728, {2,9,6,4,2}*1728, {2,3,6,4,2}*1728a, {2,6,2,2,18}*1728, {2,6,2,18,2}*1728, {2,6,18,2,2}*1728a, {2,18,2,2,6}*1728, {2,18,2,6,2}*1728, {2,18,6,2,2}*1728a, {2,18,6,2,2}*1728b, {6,18,2,2,2}*1728a, {6,18,2,2,2}*1728b, {18,6,2,2,2}*1728a, {2,6,6,2,2}*1728b, {2,6,6,2,2}*1728c, {2,6,6,6,2}*1728a, {6,6,2,2,2}*1728a, {6,6,2,2,2}*1728b, {2,3,2,6,12}*1728a, {2,3,2,6,12}*1728b, {2,3,2,12,6}*1728a, {2,3,2,12,6}*1728b, {2,3,6,2,12}*1728, {6,3,2,2,12}*1728, {6,3,2,12,2}*1728, {6,3,2,4,6}*1728a, {6,3,2,6,4}*1728a, {6,3,6,2,4}*1728, {2,3,6,12,2}*1728b, {2,3,2,6,12}*1728c, {2,3,2,12,6}*1728c, {2,3,6,4,6}*1728, {6,3,6,4,2}*1728, {2,3,6,6,4}*1728d, {2,3,2,4,4}*1728, {2,3,2,4,6}*1728, {2,3,2,6,4}*1728, {2,3,6,4,2}*1728b, {2,6,2,6,6}*1728a, {2,6,2,6,6}*1728b, {2,6,2,6,6}*1728c, {2,6,6,2,2}*1728d, {2,6,6,2,6}*1728a, {2,6,6,2,6}*1728c, {2,6,6,6,2}*1728b, {2,6,6,6,2}*1728c, {2,6,6,6,2}*1728e, {2,6,6,6,2}*1728g, {6,6,2,2,2}*1728d, {6,6,2,2,6}*1728a, {6,6,2,2,6}*1728b, {6,6,2,6,2}*1728a, {6,6,2,6,2}*1728b, {6,6,6,2,2}*1728b, {6,6,6,2,2}*1728d, {6,6,6,2,2}*1728e, {6,6,6,2,2}*1728f
19-fold covers : {2,3,2,2,38}*1824, {2,3,2,38,2}*1824, {2,57,2,2,2}*1824
20-fold covers : {2,15,2,4,4}*1920, {2,3,2,4,20}*1920, {2,3,2,20,4}*1920, {2,15,2,2,8}*1920, {2,15,2,8,2}*1920, {2,3,2,8,10}*1920, {2,3,2,10,8}*1920, {2,3,2,2,40}*1920, {2,3,2,40,2}*1920, {2,30,2,2,4}*1920, {2,30,2,4,2}*1920, {2,30,4,2,2}*1920a, {4,30,2,2,2}*1920a, {2,60,2,2,2}*1920, {2,6,2,4,10}*1920, {2,6,2,10,4}*1920, {2,6,4,2,10}*1920a, {2,6,4,10,2}*1920, {2,6,10,2,4}*1920, {2,6,10,4,2}*1920, {4,6,2,2,10}*1920a, {4,6,2,10,2}*1920a, {4,6,10,2,2}*1920a, {10,6,2,2,4}*1920, {10,6,2,4,2}*1920, {10,6,4,2,2}*1920a, {2,12,2,2,10}*1920, {2,12,2,10,2}*1920, {2,12,10,2,2}*1920, {10,12,2,2,2}*1920, {2,6,2,2,20}*1920, {2,6,2,20,2}*1920, {2,6,20,2,2}*1920a, {20,6,2,2,2}*1920a, {2,3,4,2,10}*1920, {2,3,4,10,2}*1920, {4,3,2,2,10}*1920, {4,3,2,10,2}*1920, {2,15,4,2,2}*1920, {4,15,2,2,2}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := (6,7);;
s4 := (8,9);;
s5 := (10,11);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(11)!(1,2);
s1 := Sym(11)!(4,5);
s2 := Sym(11)!(3,4);
s3 := Sym(11)!(6,7);
s4 := Sym(11)!(8,9);
s5 := Sym(11)!(10,11);
poly := sub<Sym(11)|s0,s1,s2,s3,s4,s5>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s1*s2*s1*s2*s1*s2 >;

```

to this polytope