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# Polytope of Type {2,2,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6}*192a
if this polytope has a name.
Group : SmallGroup(192,1514)
Rank : 5
Schlafli Type : {2,2,4,6}
Number of vertices, edges, etc : 2, 2, 4, 12, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,4,6,2} of size 384
{2,2,4,6,3} of size 576
{2,2,4,6,4} of size 768
{2,2,4,6,3} of size 768
{2,2,4,6,4} of size 768
{2,2,4,6,6} of size 1152
{2,2,4,6,6} of size 1152
{2,2,4,6,6} of size 1152
{2,2,4,6,9} of size 1728
{2,2,4,6,3} of size 1728
{2,2,4,6,10} of size 1920
{2,2,4,6,5} of size 1920
{2,2,4,6,5} of size 1920
Vertex Figure Of :
{2,2,2,4,6} of size 384
{3,2,2,4,6} of size 576
{4,2,2,4,6} of size 768
{5,2,2,4,6} of size 960
{6,2,2,4,6} of size 1152
{7,2,2,4,6} of size 1344
{9,2,2,4,6} of size 1728
{10,2,2,4,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,2,6}*96
3-fold quotients : {2,2,4,2}*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, {2,4,4,6}*384, {4,2,4,6}*384a, {2,2,8,6}*384
3-fold covers : {2,2,4,18}*576a, {2,2,12,6}*576a, {2,6,4,6}*576, {6,2,4,6}*576a, {2,2,12,6}*576c
4-fold covers : {4,4,4,6}*768, {2,4,4,12}*768, {4,2,4,12}*768a, {2,4,8,6}*768a, {2,8,4,6}*768a, {2,2,8,12}*768a, {2,2,4,24}*768a, {2,4,8,6}*768b, {2,8,4,6}*768b, {2,2,8,12}*768b, {2,2,4,24}*768b, {2,4,4,6}*768a, {2,2,4,12}*768a, {4,2,8,6}*768, {8,2,4,6}*768a, {2,2,16,6}*768, {2,2,4,6}*768b
5-fold covers : {2,2,20,6}*960a, {2,10,4,6}*960, {10,2,4,6}*960a, {2,2,4,30}*960a
6-fold covers : {2,4,4,18}*1152, {2,2,4,36}*1152a, {6,4,4,6}*1152, {2,4,12,6}*1152a, {2,6,4,12}*1152, {2,12,4,6}*1152, {6,2,4,12}*1152a, {2,4,12,6}*1152c, {2,2,12,12}*1152a, {2,2,12,12}*1152b, {4,2,4,18}*1152a, {4,6,4,6}*1152a, {4,2,12,6}*1152a, {4,2,12,6}*1152b, {12,2,4,6}*1152a, {2,2,8,18}*1152, {2,6,8,6}*1152, {6,2,8,6}*1152, {2,2,24,6}*1152a, {2,2,24,6}*1152b
7-fold covers : {2,2,28,6}*1344a, {2,14,4,6}*1344, {14,2,4,6}*1344a, {2,2,4,42}*1344a
9-fold covers : {2,2,4,54}*1728a, {2,2,12,18}*1728a, {2,2,36,6}*1728a, {2,2,12,6}*1728b, {2,6,4,18}*1728, {2,18,4,6}*1728, {6,2,4,18}*1728a, {18,2,4,6}*1728a, {2,6,12,6}*1728a, {2,2,12,18}*1728b, {2,2,12,6}*1728c, {2,6,12,6}*1728b, {2,6,12,6}*1728c, {6,2,12,6}*1728a, {6,6,4,6}*1728a, {6,6,4,6}*1728b, {2,2,12,6}*1728g, {6,6,4,6}*1728c, {2,6,12,6}*1728f, {2,6,12,6}*1728g, {6,2,12,6}*1728c, {2,2,4,6}*1728b, {2,6,4,6}*1728b
10-fold covers : {2,4,4,30}*1920, {2,2,4,60}*1920a, {10,4,4,6}*1920, {2,10,4,12}*1920, {10,2,4,12}*1920a, {2,4,20,6}*1920, {2,20,4,6}*1920, {2,2,20,12}*1920, {4,2,4,30}*1920a, {4,10,4,6}*1920, {4,2,20,6}*1920a, {20,2,4,6}*1920a, {2,2,8,30}*1920, {2,10,8,6}*1920, {10,2,8,6}*1920, {2,2,40,6}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 9)(10,13)(11,14);;
s3 := ( 5, 6)( 7,11)( 8,10)( 9,12)(13,16)(14,15);;
s4 := ( 5, 7)( 6,10)( 9,13)(12,15);;
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, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

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

```

to this polytope