Questions?
See the FAQ
or other info.

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

Atlas Canonical Name : {2,2,2,4,3}*192
if this polytope has a name.
Group : SmallGroup(192,1537)
Rank : 6
Schlafli Type : {2,2,2,4,3}
Number of vertices, edges, etc : 2, 2, 2, 4, 6, 3
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,2,4,3,2} of size 384
{2,2,2,4,3,4} of size 768
{2,2,2,4,3,6} of size 1152
Vertex Figure Of :
{2,2,2,2,4,3} of size 384
{3,2,2,2,4,3} of size 576
{4,2,2,2,4,3} of size 768
{5,2,2,2,4,3} of size 960
{6,2,2,2,4,3} of size 1152
{7,2,2,2,4,3} of size 1344
{9,2,2,2,4,3} of size 1728
{10,2,2,2,4,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,4,2,4,3}*384, {4,2,2,4,3}*384, {2,2,2,4,3}*384, {2,2,2,4,6}*384b, {2,2,2,4,6}*384c
3-fold covers : {2,2,2,4,9}*576, {2,6,2,4,3}*576, {6,2,2,4,3}*576
4-fold covers : {4,4,2,4,3}*768, {2,2,4,4,3}*768a, {2,8,2,4,3}*768, {8,2,2,4,3}*768, {2,2,2,4,12}*768b, {2,2,2,4,12}*768c, {2,2,4,4,3}*768b, {2,4,2,4,3}*768, {2,4,2,4,6}*768b, {2,4,2,4,6}*768c, {4,2,2,4,3}*768, {4,2,2,4,6}*768b, {4,2,2,4,6}*768c, {2,2,2,8,3}*768, {2,2,2,4,6}*768
5-fold covers : {2,10,2,4,3}*960, {10,2,2,4,3}*960, {2,2,2,4,15}*960
6-fold covers : {2,4,2,4,9}*1152, {4,2,2,4,9}*1152, {2,2,2,4,9}*1152, {2,2,2,4,18}*1152b, {2,2,2,4,18}*1152c, {2,12,2,4,3}*1152, {12,2,2,4,3}*1152, {4,6,2,4,3}*1152a, {6,4,2,4,3}*1152a, {2,2,2,12,3}*1152, {2,2,2,12,6}*1152d, {2,2,6,4,3}*1152, {2,6,2,4,3}*1152, {2,6,2,4,6}*1152b, {2,6,2,4,6}*1152c, {6,2,2,4,3}*1152, {6,2,2,4,6}*1152b, {6,2,2,4,6}*1152c
7-fold covers : {2,14,2,4,3}*1344, {14,2,2,4,3}*1344, {2,2,2,4,21}*1344
9-fold covers : {2,2,2,4,27}*1728, {2,18,2,4,3}*1728, {18,2,2,4,3}*1728, {2,6,2,4,9}*1728, {6,2,2,4,9}*1728, {6,6,2,4,3}*1728a, {6,6,2,4,3}*1728b, {6,6,2,4,3}*1728c
10-fold covers : {2,20,2,4,3}*1920, {20,2,2,4,3}*1920, {4,10,2,4,3}*1920, {10,4,2,4,3}*1920, {2,4,2,4,15}*1920, {4,2,2,4,15}*1920, {2,2,2,20,6}*1920b, {2,2,10,4,3}*1920, {2,10,2,4,3}*1920, {2,10,2,4,6}*1920b, {2,10,2,4,6}*1920c, {10,2,2,4,3}*1920, {10,2,2,4,6}*1920b, {10,2,2,4,6}*1920c, {2,2,2,4,15}*1920, {2,2,2,4,30}*1920b, {2,2,2,4,30}*1920c
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 7, 8)( 9,10);;
s4 := (8,9);;
s5 := ( 9,10);;
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, 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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s3*s4*s3*s4,
s5*s3*s4*s5*s3*s4*s5*s3*s4 ];;
poly := F / rels;;

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

```

to this polytope