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# Polytope of Type {2,2,2,12}

Atlas Canonical Name : {2,2,2,12}*192
if this polytope has a name.
Group : SmallGroup(192,1512)
Rank : 5
Schlafli Type : {2,2,2,12}
Number of vertices, edges, etc : 2, 2, 2, 12, 12
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,2,12,2} of size 384
{2,2,2,12,4} of size 768
{2,2,2,12,4} of size 768
{2,2,2,12,4} of size 768
{2,2,2,12,3} of size 768
{2,2,2,12,6} of size 1152
{2,2,2,12,6} of size 1152
{2,2,2,12,6} of size 1152
{2,2,2,12,3} of size 1152
{2,2,2,12,6} of size 1152
{2,2,2,12,4} of size 1728
{2,2,2,12,6} of size 1728
{2,2,2,12,6} of size 1728
{2,2,2,12,6} of size 1728
{2,2,2,12,10} of size 1920
Vertex Figure Of :
{2,2,2,2,12} of size 384
{3,2,2,2,12} of size 576
{4,2,2,2,12} of size 768
{5,2,2,2,12} of size 960
{6,2,2,2,12} of size 1152
{7,2,2,2,12} of size 1344
{9,2,2,2,12} of size 1728
{10,2,2,2,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,6}*96
3-fold quotients : {2,2,2,4}*64
4-fold quotients : {2,2,2,3}*48
6-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,4,12}*384a, {2,4,2,12}*384, {4,2,2,12}*384, {2,2,2,24}*384
3-fold covers : {2,2,2,36}*576, {2,2,6,12}*576a, {2,2,6,12}*576b, {2,6,2,12}*576, {6,2,2,12}*576
4-fold covers : {2,4,4,12}*768, {4,4,2,12}*768, {4,2,4,12}*768a, {2,2,8,12}*768a, {2,2,4,24}*768a, {2,2,8,12}*768b, {2,2,4,24}*768b, {2,2,4,12}*768a, {2,8,2,12}*768, {8,2,2,12}*768, {2,4,2,24}*768, {4,2,2,24}*768, {2,2,2,48}*768, {2,2,4,12}*768b
5-fold covers : {2,2,10,12}*960, {2,10,2,12}*960, {10,2,2,12}*960, {2,2,2,60}*960
6-fold covers : {2,2,4,36}*1152a, {2,6,4,12}*1152, {6,2,4,12}*1152a, {2,2,12,12}*1152a, {2,2,12,12}*1152b, {2,4,2,36}*1152, {4,2,2,36}*1152, {4,2,6,12}*1152b, {4,2,6,12}*1152c, {4,6,2,12}*1152a, {6,4,2,12}*1152a, {2,4,6,12}*1152b, {2,4,6,12}*1152c, {2,12,2,12}*1152, {12,2,2,12}*1152, {2,2,2,72}*1152, {2,2,6,24}*1152b, {2,2,6,24}*1152c, {2,6,2,24}*1152, {6,2,2,24}*1152
7-fold covers : {2,2,14,12}*1344, {2,14,2,12}*1344, {14,2,2,12}*1344, {2,2,2,84}*1344
9-fold covers : {2,2,2,108}*1728, {2,2,18,12}*1728a, {2,18,2,12}*1728, {18,2,2,12}*1728, {2,2,6,36}*1728a, {2,2,6,36}*1728b, {2,6,2,36}*1728, {6,2,2,36}*1728, {2,2,6,12}*1728a, {2,2,6,12}*1728b, {2,6,6,12}*1728a, {2,6,6,12}*1728b, {2,6,6,12}*1728c, {2,6,6,12}*1728d, {6,2,6,12}*1728a, {6,2,6,12}*1728b, {6,6,2,12}*1728a, {6,6,2,12}*1728b, {6,6,2,12}*1728c, {2,2,6,12}*1728g, {2,6,6,12}*1728e, {2,2,6,12}*1728i
10-fold covers : {2,2,4,60}*1920a, {2,10,4,12}*1920, {10,2,4,12}*1920a, {2,2,20,12}*1920, {2,4,2,60}*1920, {4,2,2,60}*1920, {4,2,10,12}*1920, {4,10,2,12}*1920, {10,4,2,12}*1920, {2,4,10,12}*1920, {2,20,2,12}*1920, {20,2,2,12}*1920, {2,2,2,120}*1920, {2,2,10,24}*1920, {2,10,2,24}*1920, {10,2,2,24}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 8, 9)(10,11)(13,16)(14,15)(17,18);;
s4 := ( 7,13)( 8,10)( 9,17)(11,14)(12,15)(16,18);;
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, 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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(18)!(1,2);
s1 := Sym(18)!(3,4);
s2 := Sym(18)!(5,6);
s3 := Sym(18)!( 8, 9)(10,11)(13,16)(14,15)(17,18);
s4 := Sym(18)!( 7,13)( 8,10)( 9,17)(11,14)(12,15)(16,18);
poly := sub<Sym(18)|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,
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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

```

to this polytope