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# Polytope of Type {4,6,2}

Atlas Canonical Name : {4,6,2}*96b
if this polytope has a name.
Group : SmallGroup(96,226)
Rank : 4
Schlafli Type : {4,6,2}
Number of vertices, edges, etc : 4, 12, 6, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,6,2,2} of size 192
{4,6,2,3} of size 288
{4,6,2,4} of size 384
{4,6,2,5} of size 480
{4,6,2,6} of size 576
{4,6,2,7} of size 672
{4,6,2,8} of size 768
{4,6,2,9} of size 864
{4,6,2,10} of size 960
{4,6,2,11} of size 1056
{4,6,2,12} of size 1152
{4,6,2,13} of size 1248
{4,6,2,14} of size 1344
{4,6,2,15} of size 1440
{4,6,2,17} of size 1632
{4,6,2,18} of size 1728
{4,6,2,19} of size 1824
{4,6,2,20} of size 1920
Vertex Figure Of :
{2,4,6,2} of size 192
{4,4,6,2} of size 768
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,6,2}*192
3-fold covers : {4,18,2}*288c, {4,6,6}*288f, {12,6,2}*288d
4-fold covers : {8,6,2}*384a, {4,12,2}*384b, {4,6,4}*384b, {4,6,2}*384b, {4,12,2}*384c, {8,6,2}*384b, {8,6,2}*384c, {4,6,4}*384f
5-fold covers : {20,6,2}*480b, {4,30,2}*480c
6-fold covers : {4,18,2}*576, {4,6,6}*576a, {4,6,6}*576b, {12,6,2}*576a, {12,6,2}*576b
7-fold covers : {28,6,2}*672b, {4,42,2}*672c
8-fold covers : {8,12,2}*768c, {8,12,2}*768d, {4,12,4}*768f, {4,12,2}*768d, {4,6,4}*768d, {4,12,4}*768h, {8,6,2}*768d, {8,6,2}*768e, {4,6,2}*768a, {8,12,2}*768e, {8,12,2}*768f, {4,24,2}*768c, {4,24,2}*768d, {8,6,2}*768f, {8,12,2}*768g, {8,12,2}*768h, {4,6,8}*768a, {8,6,2}*768g, {8,6,4}*768b, {8,6,4}*768c, {4,6,2}*768b, {4,24,2}*768e, {4,12,2}*768e, {4,24,2}*768f, {4,6,8}*768f, {4,6,8}*768h, {4,6,4}*768i, {4,6,4}*768l
9-fold covers : {4,54,2}*864c, {36,6,2}*864c, {4,18,6}*864e, {12,18,2}*864c, {4,6,6}*864f, {12,6,2}*864d, {12,6,6}*864h
10-fold covers : {4,6,10}*960e, {20,6,2}*960c, {4,30,2}*960
11-fold covers : {44,6,2}*1056b, {4,66,2}*1056c
12-fold covers : {8,18,2}*1152a, {4,36,2}*1152b, {4,18,4}*1152b, {4,18,2}*1152b, {4,36,2}*1152c, {8,18,2}*1152b, {8,18,2}*1152c, {24,6,2}*1152a, {8,6,6}*1152a, {4,18,4}*1152f, {4,12,6}*1152e, {4,12,6}*1152f, {12,12,2}*1152f, {12,12,2}*1152g, {4,6,12}*1152a, {12,6,2}*1152b, {12,12,2}*1152i, {4,6,6}*1152d, {4,6,6}*1152e, {4,12,6}*1152h, {4,12,6}*1152i, {12,6,4}*1152b, {12,6,4}*1152c, {24,6,2}*1152b, {24,6,2}*1152c, {24,6,2}*1152d, {8,6,6}*1152b, {8,6,6}*1152c, {24,6,2}*1152e, {8,6,6}*1152d, {8,6,6}*1152e, {4,6,12}*1152d, {12,6,2}*1152f, {12,12,2}*1152k, {4,6,6}*1152h, {12,12,2}*1152l, {4,6,12}*1152h, {12,6,4}*1152e
13-fold covers : {52,6,2}*1248b, {4,78,2}*1248c
14-fold covers : {4,6,14}*1344, {28,6,2}*1344, {4,42,2}*1344
15-fold covers : {20,18,2}*1440b, {4,90,2}*1440c, {20,6,6}*1440d, {4,30,6}*1440f, {12,30,2}*1440d, {60,6,2}*1440d
17-fold covers : {68,6,2}*1632b, {4,102,2}*1632c
18-fold covers : {4,54,2}*1728, {4,6,18}*1728, {36,6,2}*1728, {4,18,6}*1728a, {4,18,6}*1728b, {12,18,2}*1728a, {12,18,2}*1728b, {4,6,6}*1728a, {4,6,6}*1728b, {12,6,2}*1728a, {12,6,2}*1728b, {4,6,6}*1728c, {12,6,6}*1728a, {12,6,6}*1728b, {12,6,6}*1728c, {12,6,6}*1728d, {12,6,2}*1728c
19-fold covers : {76,6,2}*1824b, {4,114,2}*1824c
20-fold covers : {40,6,2}*1920a, {8,30,2}*1920a, {4,12,10}*1920b, {20,12,2}*1920b, {4,6,20}*1920a, {20,6,2}*1920a, {4,6,10}*1920b, {4,12,10}*1920c, {20,6,4}*1920b, {40,6,2}*1920b, {8,6,10}*1920a, {40,6,2}*1920c, {8,6,10}*1920b, {20,12,2}*1920c, {4,60,2}*1920b, {4,30,4}*1920b, {4,30,2}*1920b, {4,60,2}*1920c, {8,30,2}*1920b, {8,30,2}*1920c, {20,6,4}*1920c, {4,30,4}*1920f
Permutation Representation (GAP) :
```s0 := (4,6);;
s1 := (3,4)(5,6);;
s2 := (1,3)(2,5)(4,6);;
s3 := (7,8);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;

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

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s2 >;

```

to this polytope