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# Polytope of Type {6,2,4}

Atlas Canonical Name : {6,2,4}*96
if this polytope has a name.
Group : SmallGroup(96,209)
Rank : 4
Schlafli Type : {6,2,4}
Number of vertices, edges, etc : 6, 6, 4, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,2,4,2} of size 192
{6,2,4,3} of size 288
{6,2,4,4} of size 384
{6,2,4,6} of size 576
{6,2,4,3} of size 576
{6,2,4,6} of size 576
{6,2,4,6} of size 576
{6,2,4,8} of size 768
{6,2,4,8} of size 768
{6,2,4,4} of size 768
{6,2,4,9} of size 864
{6,2,4,4} of size 864
{6,2,4,6} of size 864
{6,2,4,10} of size 960
{6,2,4,12} of size 1152
{6,2,4,12} of size 1152
{6,2,4,12} of size 1152
{6,2,4,6} of size 1152
{6,2,4,14} of size 1344
{6,2,4,5} of size 1440
{6,2,4,6} of size 1440
{6,2,4,15} of size 1440
{6,2,4,18} of size 1728
{6,2,4,9} of size 1728
{6,2,4,18} of size 1728
{6,2,4,18} of size 1728
{6,2,4,4} of size 1728
{6,2,4,6} of size 1728
{6,2,4,20} of size 1920
{6,2,4,5} of size 1920
Vertex Figure Of :
{2,6,2,4} of size 192
{3,6,2,4} of size 288
{4,6,2,4} of size 384
{3,6,2,4} of size 384
{4,6,2,4} of size 384
{4,6,2,4} of size 384
{4,6,2,4} of size 576
{6,6,2,4} of size 576
{6,6,2,4} of size 576
{6,6,2,4} of size 576
{8,6,2,4} of size 768
{4,6,2,4} of size 768
{6,6,2,4} of size 768
{9,6,2,4} of size 864
{3,6,2,4} of size 864
{6,6,2,4} of size 864
{4,6,2,4} of size 960
{5,6,2,4} of size 960
{6,6,2,4} of size 960
{5,6,2,4} of size 960
{5,6,2,4} of size 960
{10,6,2,4} of size 960
{12,6,2,4} of size 1152
{12,6,2,4} of size 1152
{12,6,2,4} of size 1152
{4,6,2,4} of size 1152
{3,6,2,4} of size 1152
{12,6,2,4} of size 1152
{14,6,2,4} of size 1344
{15,6,2,4} of size 1440
{4,6,2,4} of size 1728
{12,6,2,4} of size 1728
{12,6,2,4} of size 1728
{18,6,2,4} of size 1728
{18,6,2,4} of size 1728
{6,6,2,4} of size 1728
{6,6,2,4} of size 1728
{6,6,2,4} of size 1728
{12,6,2,4} of size 1728
{6,6,2,4} of size 1728
{20,6,2,4} of size 1920
{15,6,2,4} of size 1920
{20,6,2,4} of size 1920
{4,6,2,4} of size 1920
{4,6,2,4} of size 1920
{4,6,2,4} of size 1920
{5,6,2,4} of size 1920
{6,6,2,4} of size 1920
{6,6,2,4} of size 1920
{6,6,2,4} of size 1920
{10,6,2,4} of size 1920
{10,6,2,4} of size 1920
{5,6,2,4} of size 1920
{10,6,2,4} of size 1920
{10,6,2,4} of size 1920
{10,6,2,4} of size 1920
{10,6,2,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,4}*48, {6,2,2}*48
3-fold quotients : {2,2,4}*32
4-fold quotients : {3,2,2}*24
6-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,2,4}*192, {6,4,4}*192, {6,2,8}*192
3-fold covers : {18,2,4}*288, {6,2,12}*288, {6,6,4}*288a, {6,6,4}*288c
4-fold covers : {12,4,4}*384, {24,2,4}*384, {12,2,8}*384, {6,4,8}*384a, {6,8,4}*384a, {6,4,8}*384b, {6,8,4}*384b, {6,4,4}*384a, {6,2,16}*384, {6,4,4}*384d
5-fold covers : {6,2,20}*480, {6,10,4}*480, {30,2,4}*480
6-fold covers : {36,2,4}*576, {18,4,4}*576, {18,2,8}*576, {12,2,12}*576, {6,4,12}*576, {6,12,4}*576a, {12,6,4}*576a, {6,2,24}*576, {6,6,8}*576a, {12,6,4}*576b, {6,6,8}*576c, {6,12,4}*576c
7-fold covers : {6,2,28}*672, {6,14,4}*672, {42,2,4}*672
8-fold covers : {6,4,8}*768a, {6,8,4}*768a, {6,8,8}*768a, {6,8,8}*768b, {6,8,8}*768c, {6,8,8}*768d, {24,2,8}*768, {12,4,8}*768a, {24,4,4}*768a, {12,4,8}*768b, {24,4,4}*768b, {12,8,4}*768a, {12,4,4}*768a, {12,4,4}*768b, {12,8,4}*768b, {12,8,4}*768c, {12,8,4}*768d, {6,4,16}*768a, {6,16,4}*768a, {6,4,16}*768b, {6,16,4}*768b, {6,4,4}*768a, {6,4,8}*768b, {6,8,4}*768b, {12,2,16}*768, {48,2,4}*768, {6,2,32}*768, {6,4,4}*768e, {12,4,4}*768e, {12,4,4}*768f, {6,8,4}*768c, {6,4,8}*768c, {6,8,4}*768d
9-fold covers : {54,2,4}*864, {6,2,36}*864, {18,2,12}*864, {6,6,12}*864a, {6,18,4}*864a, {18,6,4}*864a, {6,6,4}*864b, {18,6,4}*864b, {6,6,4}*864c, {6,6,12}*864b, {6,6,12}*864c, {6,6,12}*864e, {6,6,4}*864h, {6,6,12}*864f, {6,6,4}*864j, {6,6,4}*864k
10-fold covers : {12,2,20}*960, {6,4,20}*960, {6,20,4}*960, {12,10,4}*960, {6,2,40}*960, {6,10,8}*960, {60,2,4}*960, {30,4,4}*960, {30,2,8}*960
11-fold covers : {6,2,44}*1056, {6,22,4}*1056, {66,2,4}*1056
12-fold covers : {36,4,4}*1152, {12,12,4}*1152b, {12,12,4}*1152c, {12,4,12}*1152, {18,4,8}*1152a, {18,8,4}*1152a, {6,8,12}*1152a, {6,12,8}*1152b, {6,12,8}*1152c, {6,24,4}*1152a, {6,4,24}*1152a, {6,24,4}*1152c, {18,4,8}*1152b, {18,8,4}*1152b, {6,8,12}*1152b, {6,12,8}*1152e, {6,12,8}*1152f, {6,24,4}*1152d, {6,4,24}*1152b, {6,24,4}*1152f, {18,4,4}*1152a, {6,4,12}*1152a, {6,12,4}*1152b, {6,12,4}*1152c, {36,2,8}*1152, {72,2,4}*1152, {12,6,8}*1152b, {12,6,8}*1152c, {24,6,4}*1152b, {24,6,4}*1152c, {12,2,24}*1152, {24,2,12}*1152, {18,2,16}*1152, {6,6,16}*1152b, {6,6,16}*1152c, {6,2,48}*1152, {18,4,4}*1152d, {6,4,12}*1152b, {6,4,12}*1152c, {6,6,4}*1152c, {6,6,12}*1152b, {6,12,4}*1152i, {12,6,4}*1152b, {6,6,4}*1152f, {6,12,4}*1152j
13-fold covers : {6,2,52}*1248, {6,26,4}*1248, {78,2,4}*1248
14-fold covers : {12,2,28}*1344, {12,14,4}*1344, {6,4,28}*1344, {6,28,4}*1344, {6,2,56}*1344, {6,14,8}*1344, {84,2,4}*1344, {42,4,4}*1344, {42,2,8}*1344
15-fold covers : {18,2,20}*1440, {18,10,4}*1440, {90,2,4}*1440, {6,10,12}*1440, {6,6,20}*1440a, {6,6,20}*1440c, {6,30,4}*1440a, {30,2,12}*1440, {6,2,60}*1440, {6,30,4}*1440b, {30,6,4}*1440b, {30,6,4}*1440c
17-fold covers : {6,2,68}*1632, {6,34,4}*1632, {102,2,4}*1632
18-fold covers : {108,2,4}*1728, {54,4,4}*1728, {54,2,8}*1728, {12,2,36}*1728, {36,2,12}*1728, {12,6,12}*1728a, {36,6,4}*1728a, {12,18,4}*1728a, {18,4,12}*1728, {18,12,4}*1728a, {6,4,36}*1728, {6,36,4}*1728a, {12,6,4}*1728a, {6,12,4}*1728b, {6,12,12}*1728a, {6,2,72}*1728, {18,2,24}*1728, {6,6,24}*1728a, {6,18,8}*1728a, {18,6,8}*1728a, {6,6,8}*1728b, {36,6,4}*1728b, {12,6,4}*1728b, {18,6,8}*1728b, {6,6,8}*1728c, {18,12,4}*1728b, {6,12,4}*1728c, {6,6,24}*1728b, {6,6,24}*1728c, {6,6,24}*1728e, {12,6,12}*1728b, {12,6,12}*1728d, {12,6,12}*1728e, {12,6,12}*1728f, {6,12,12}*1728b, {6,12,12}*1728c, {6,12,12}*1728e, {6,6,8}*1728e, {6,6,24}*1728f, {6,12,4}*1728j, {6,12,12}*1728g, {12,6,4}*1728h, {6,6,8}*1728f, {12,6,4}*1728k, {12,6,4}*1728l, {6,6,8}*1728g, {6,4,4}*1728b, {6,4,4}*1728c, {6,4,12}*1728b, {6,12,4}*1728n, {6,12,4}*1728p, {12,4,4}*1728c, {12,6,4}*1728n
19-fold covers : {6,2,76}*1824, {6,38,4}*1824, {114,2,4}*1824
20-fold covers : {60,4,4}*1920, {12,20,4}*1920, {12,4,20}*1920, {30,4,8}*1920a, {30,8,4}*1920a, {6,8,20}*1920a, {6,20,8}*1920a, {6,4,40}*1920a, {6,40,4}*1920a, {30,4,8}*1920b, {30,8,4}*1920b, {6,8,20}*1920b, {6,20,8}*1920b, {6,4,40}*1920b, {6,40,4}*1920b, {30,4,4}*1920a, {6,4,20}*1920a, {6,20,4}*1920a, {60,2,8}*1920, {120,2,4}*1920, {12,10,8}*1920, {24,10,4}*1920, {12,2,40}*1920, {24,2,20}*1920, {30,2,16}*1920, {6,10,16}*1920, {6,2,80}*1920, {6,4,20}*1920b, {6,20,4}*1920c, {30,4,4}*1920d
Permutation Representation (GAP) :
```s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (8,9);;
s3 := ( 7, 8)( 9,10);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope