Questions?
See the FAQ
or other info.

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

Atlas Canonical Name : {2,2,4,3}*96
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 5
Schlafli Type : {2,2,4,3}
Number of vertices, edges, etc : 2, 2, 4, 6, 3
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,4,3,2} of size 192
{2,2,4,3,4} of size 384
{2,2,4,3,6} of size 576
{2,2,4,3,4} of size 768
{2,2,4,3,6} of size 1728
Vertex Figure Of :
{2,2,2,4,3} of size 192
{3,2,2,4,3} of size 288
{4,2,2,4,3} of size 384
{5,2,2,4,3} of size 480
{6,2,2,4,3} of size 576
{7,2,2,4,3} of size 672
{8,2,2,4,3} of size 768
{9,2,2,4,3} of size 864
{10,2,2,4,3} of size 960
{11,2,2,4,3} of size 1056
{12,2,2,4,3} of size 1152
{13,2,2,4,3} of size 1248
{14,2,2,4,3} of size 1344
{15,2,2,4,3} of size 1440
{17,2,2,4,3} of size 1632
{18,2,2,4,3} of size 1728
{19,2,2,4,3} of size 1824
{20,2,2,4,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,2,4,3}*192, {2,2,4,3}*192, {2,2,4,6}*192b, {2,2,4,6}*192c
3-fold covers : {2,2,4,9}*288, {6,2,4,3}*288
4-fold covers : {2,4,4,3}*384a, {8,2,4,3}*384, {2,2,4,12}*384b, {2,2,4,12}*384c, {2,4,4,3}*384b, {4,2,4,3}*384, {4,2,4,6}*384b, {4,2,4,6}*384c, {2,2,8,3}*384, {2,2,4,6}*384
5-fold covers : {10,2,4,3}*480, {2,2,4,15}*480
6-fold covers : {4,2,4,9}*576, {2,2,4,9}*576, {2,2,4,18}*576b, {2,2,4,18}*576c, {12,2,4,3}*576, {2,2,12,3}*576, {2,2,12,6}*576d, {2,6,4,3}*576, {6,2,4,3}*576, {6,2,4,6}*576b, {6,2,4,6}*576c
7-fold covers : {14,2,4,3}*672, {2,2,4,21}*672
8-fold covers : {4,4,4,3}*768a, {2,4,4,3}*768a, {16,2,4,3}*768, {4,4,4,3}*768b, {4,2,4,12}*768b, {4,2,4,12}*768c, {2,2,8,3}*768, {2,2,8,6}*768a, {2,2,4,6}*768a, {2,4,4,3}*768b, {2,4,4,6}*768b, {2,4,4,6}*768c, {2,2,4,24}*768c, {2,2,4,24}*768d, {2,4,8,3}*768, {2,8,4,3}*768, {8,2,4,3}*768, {8,2,4,6}*768b, {8,2,4,6}*768c, {4,2,8,3}*768, {2,2,4,12}*768b, {2,2,4,6}*768b, {2,2,4,12}*768c, {2,4,4,6}*768d, {4,2,4,6}*768, {2,2,8,6}*768b, {2,2,8,6}*768c
9-fold covers : {2,2,4,27}*864, {18,2,4,3}*864, {6,2,4,9}*864
10-fold covers : {20,2,4,3}*960, {4,2,4,15}*960, {2,2,20,6}*960b, {2,10,4,3}*960, {10,2,4,3}*960, {10,2,4,6}*960b, {10,2,4,6}*960c, {2,2,4,15}*960, {2,2,4,30}*960b, {2,2,4,30}*960c
11-fold covers : {22,2,4,3}*1056, {2,2,4,33}*1056
12-fold covers : {2,4,4,9}*1152a, {8,2,4,9}*1152, {2,2,4,36}*1152b, {2,2,4,36}*1152c, {2,4,4,9}*1152b, {4,2,4,9}*1152, {4,2,4,18}*1152b, {4,2,4,18}*1152c, {2,2,8,9}*1152, {6,4,4,3}*1152a, {24,2,4,3}*1152, {2,2,4,18}*1152, {6,2,4,12}*1152b, {6,2,4,12}*1152c, {2,12,4,3}*1152, {12,2,4,3}*1152, {12,2,4,6}*1152b, {12,2,4,6}*1152c, {4,6,4,3}*1152a, {6,4,4,3}*1152b, {4,2,12,3}*1152, {4,2,12,6}*1152d, {2,2,24,3}*1152, {2,6,8,3}*1152, {6,2,8,3}*1152, {2,4,12,3}*1152, {2,2,12,6}*1152a, {2,2,12,6}*1152b, {2,6,4,6}*1152a, {6,2,4,6}*1152
13-fold covers : {26,2,4,3}*1248, {2,2,4,39}*1248
14-fold covers : {28,2,4,3}*1344, {4,2,4,21}*1344, {2,2,28,6}*1344b, {2,14,4,3}*1344, {14,2,4,3}*1344, {14,2,4,6}*1344b, {14,2,4,6}*1344c, {2,2,4,21}*1344, {2,2,4,42}*1344b, {2,2,4,42}*1344c
15-fold covers : {10,2,4,9}*1440, {2,2,4,45}*1440, {6,2,4,15}*1440, {30,2,4,3}*1440
17-fold covers : {34,2,4,3}*1632, {2,2,4,51}*1632
18-fold covers : {4,2,4,27}*1728, {2,2,4,27}*1728, {2,2,4,54}*1728b, {2,2,4,54}*1728c, {36,2,4,3}*1728, {12,2,4,9}*1728, {2,2,36,6}*1728c, {2,18,4,3}*1728, {18,2,4,3}*1728, {18,2,4,6}*1728b, {18,2,4,6}*1728c, {2,2,12,9}*1728, {2,2,12,18}*1728c, {2,6,4,9}*1728, {6,2,4,9}*1728, {6,2,4,18}*1728b, {6,2,4,18}*1728c, {2,2,12,3}*1728, {2,2,12,6}*1728d, {2,6,12,3}*1728a, {6,6,4,3}*1728a, {6,6,4,3}*1728b, {6,6,4,3}*1728c, {2,6,12,3}*1728b, {2,6,12,6}*1728h, {6,2,12,3}*1728, {6,2,12,6}*1728d
19-fold covers : {38,2,4,3}*1824, {2,2,4,57}*1824
20-fold covers : {10,4,4,3}*1920a, {40,2,4,3}*1920, {2,4,4,15}*1920a, {8,2,4,15}*1920, {10,2,4,12}*1920b, {10,2,4,12}*1920c, {2,20,4,3}*1920, {20,2,4,3}*1920, {20,2,4,6}*1920b, {20,2,4,6}*1920c, {4,10,4,3}*1920, {10,4,4,3}*1920b, {4,2,20,6}*1920b, {2,10,8,3}*1920, {10,2,8,3}*1920, {2,2,4,60}*1920b, {2,2,4,60}*1920c, {2,4,4,15}*1920b, {4,2,4,15}*1920, {4,2,4,30}*1920b, {4,2,4,30}*1920c, {2,2,8,15}*1920, {2,2,20,6}*1920a, {2,10,4,6}*1920, {10,2,4,6}*1920, {2,2,4,30}*1920
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6)(7,8);;
s3 := (6,7);;
s4 := (7,8);;
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, s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;

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

```

to this polytope