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

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

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

```

to this polytope