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

Atlas Canonical Name : {6,2,2,2}*96
if this polytope has a name.
Group : SmallGroup(96,230)
Rank : 5
Schlafli Type : {6,2,2,2}
Number of vertices, edges, etc : 6, 6, 2, 2, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,2,2,2,2} of size 192
{6,2,2,2,3} of size 288
{6,2,2,2,4} of size 384
{6,2,2,2,5} of size 480
{6,2,2,2,6} of size 576
{6,2,2,2,7} of size 672
{6,2,2,2,8} of size 768
{6,2,2,2,9} of size 864
{6,2,2,2,10} of size 960
{6,2,2,2,11} of size 1056
{6,2,2,2,12} of size 1152
{6,2,2,2,13} of size 1248
{6,2,2,2,14} of size 1344
{6,2,2,2,15} of size 1440
{6,2,2,2,17} of size 1632
{6,2,2,2,18} of size 1728
{6,2,2,2,19} of size 1824
{6,2,2,2,20} of size 1920
Vertex Figure Of :
{2,6,2,2,2} of size 192
{3,6,2,2,2} of size 288
{4,6,2,2,2} of size 384
{3,6,2,2,2} of size 384
{4,6,2,2,2} of size 384
{4,6,2,2,2} of size 384
{4,6,2,2,2} of size 576
{6,6,2,2,2} of size 576
{6,6,2,2,2} of size 576
{6,6,2,2,2} of size 576
{8,6,2,2,2} of size 768
{4,6,2,2,2} of size 768
{6,6,2,2,2} of size 768
{9,6,2,2,2} of size 864
{3,6,2,2,2} of size 864
{6,6,2,2,2} of size 864
{4,6,2,2,2} of size 960
{5,6,2,2,2} of size 960
{6,6,2,2,2} of size 960
{5,6,2,2,2} of size 960
{5,6,2,2,2} of size 960
{10,6,2,2,2} of size 960
{12,6,2,2,2} of size 1152
{12,6,2,2,2} of size 1152
{12,6,2,2,2} of size 1152
{4,6,2,2,2} of size 1152
{3,6,2,2,2} of size 1152
{12,6,2,2,2} of size 1152
{14,6,2,2,2} of size 1344
{15,6,2,2,2} of size 1440
{4,6,2,2,2} of size 1728
{12,6,2,2,2} of size 1728
{12,6,2,2,2} of size 1728
{18,6,2,2,2} of size 1728
{18,6,2,2,2} of size 1728
{6,6,2,2,2} of size 1728
{6,6,2,2,2} of size 1728
{6,6,2,2,2} of size 1728
{12,6,2,2,2} of size 1728
{6,6,2,2,2} of size 1728
{20,6,2,2,2} of size 1920
{15,6,2,2,2} of size 1920
{20,6,2,2,2} of size 1920
{4,6,2,2,2} of size 1920
{4,6,2,2,2} of size 1920
{4,6,2,2,2} of size 1920
{5,6,2,2,2} of size 1920
{6,6,2,2,2} of size 1920
{6,6,2,2,2} of size 1920
{6,6,2,2,2} of size 1920
{10,6,2,2,2} of size 1920
{10,6,2,2,2} of size 1920
{5,6,2,2,2} of size 1920
{10,6,2,2,2} of size 1920
{10,6,2,2,2} of size 1920
{10,6,2,2,2} of size 1920
{10,6,2,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,2,2}*48
3-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,2,2,2}*192, {6,2,2,4}*192, {6,2,4,2}*192, {6,4,2,2}*192a
3-fold covers : {18,2,2,2}*288, {6,2,2,6}*288, {6,2,6,2}*288, {6,6,2,2}*288a, {6,6,2,2}*288c
4-fold covers : {12,4,2,2}*384a, {12,2,2,4}*384, {12,2,4,2}*384, {6,2,4,4}*384, {6,4,4,2}*384, {6,4,2,4}*384a, {24,2,2,2}*384, {6,2,2,8}*384, {6,2,8,2}*384, {6,8,2,2}*384, {6,4,2,2}*384
5-fold covers : {6,2,2,10}*480, {6,2,10,2}*480, {6,10,2,2}*480, {30,2,2,2}*480
6-fold covers : {36,2,2,2}*576, {18,2,2,4}*576, {18,2,4,2}*576, {18,4,2,2}*576a, {6,2,2,12}*576, {6,2,12,2}*576, {6,12,2,2}*576a, {12,2,2,6}*576, {12,2,6,2}*576, {12,6,2,2}*576a, {12,6,2,2}*576b, {6,2,4,6}*576a, {6,2,6,4}*576a, {6,4,2,6}*576a, {6,4,6,2}*576, {6,6,2,4}*576a, {6,6,2,4}*576c, {6,6,4,2}*576a, {6,6,4,2}*576c, {6,12,2,2}*576c
7-fold covers : {6,2,2,14}*672, {6,2,14,2}*672, {6,14,2,2}*672, {42,2,2,2}*672
8-fold covers : {6,4,4,4}*768, {12,4,4,2}*768, {12,2,4,4}*768, {12,4,2,4}*768a, {6,2,4,8}*768a, {6,2,8,4}*768a, {6,4,8,2}*768a, {6,8,4,2}*768a, {12,8,2,2}*768a, {24,4,2,2}*768a, {6,2,4,8}*768b, {6,2,8,4}*768b, {6,4,8,2}*768b, {6,8,4,2}*768b, {12,8,2,2}*768b, {24,4,2,2}*768b, {6,2,4,4}*768, {6,4,4,2}*768a, {12,4,2,2}*768a, {6,4,2,8}*768a, {6,8,2,4}*768, {12,2,2,8}*768, {12,2,8,2}*768, {24,2,2,4}*768, {24,2,4,2}*768, {6,2,2,16}*768, {6,2,16,2}*768, {6,16,2,2}*768, {48,2,2,2}*768, {12,4,2,2}*768b, {6,4,2,2}*768b, {6,4,2,4}*768, {6,4,4,2}*768d, {12,4,2,2}*768c, {6,8,2,2}*768b, {6,8,2,2}*768c
9-fold covers : {54,2,2,2}*864, {6,2,2,18}*864, {6,2,18,2}*864, {6,18,2,2}*864a, {18,2,2,6}*864, {18,2,6,2}*864, {18,6,2,2}*864a, {18,6,2,2}*864b, {6,6,2,2}*864b, {6,6,2,2}*864c, {6,6,6,2}*864a, {6,2,6,6}*864a, {6,2,6,6}*864b, {6,2,6,6}*864c, {6,6,2,2}*864d, {6,6,2,6}*864a, {6,6,2,6}*864c, {6,6,6,2}*864b, {6,6,6,2}*864c, {6,6,6,2}*864e, {6,6,6,2}*864g
10-fold covers : {12,2,2,10}*960, {12,2,10,2}*960, {12,10,2,2}*960, {6,2,2,20}*960, {6,2,20,2}*960, {6,20,2,2}*960a, {6,2,4,10}*960, {6,2,10,4}*960, {6,4,2,10}*960a, {6,4,10,2}*960, {6,10,2,4}*960, {6,10,4,2}*960, {60,2,2,2}*960, {30,2,2,4}*960, {30,2,4,2}*960, {30,4,2,2}*960a
11-fold covers : {6,2,2,22}*1056, {6,2,22,2}*1056, {6,22,2,2}*1056, {66,2,2,2}*1056
12-fold covers : {18,2,4,4}*1152, {18,4,4,2}*1152, {36,4,2,2}*1152a, {6,4,4,6}*1152, {6,6,4,4}*1152b, {6,6,4,4}*1152c, {6,2,4,12}*1152a, {6,2,12,4}*1152a, {6,4,12,2}*1152, {6,12,4,2}*1152a, {12,4,2,6}*1152a, {12,4,6,2}*1152, {6,12,4,2}*1152c, {12,12,2,2}*1152a, {12,12,2,2}*1152c, {18,4,2,4}*1152a, {36,2,2,4}*1152, {36,2,4,2}*1152, {6,4,6,4}*1152a, {6,12,2,4}*1152a, {6,4,2,12}*1152a, {6,12,2,4}*1152b, {12,2,4,6}*1152a, {12,2,6,4}*1152a, {12,6,2,4}*1152b, {12,6,2,4}*1152c, {12,6,4,2}*1152b, {12,6,4,2}*1152c, {12,2,2,12}*1152, {12,2,12,2}*1152, {18,2,2,8}*1152, {18,2,8,2}*1152, {18,8,2,2}*1152, {72,2,2,2}*1152, {6,2,6,8}*1152, {6,2,8,6}*1152, {6,6,2,8}*1152a, {6,6,2,8}*1152c, {6,6,8,2}*1152a, {6,8,2,6}*1152, {6,8,6,2}*1152, {6,6,8,2}*1152c, {6,24,2,2}*1152a, {6,2,2,24}*1152, {6,2,24,2}*1152, {6,24,2,2}*1152b, {24,2,2,6}*1152, {24,2,6,2}*1152, {24,6,2,2}*1152b, {24,6,2,2}*1152c, {18,4,2,2}*1152, {6,2,4,6}*1152, {6,2,6,4}*1152, {6,2,6,6}*1152, {6,4,2,6}*1152, {6,4,6,2}*1152a, {6,4,6,2}*1152b, {6,6,2,2}*1152b, {6,6,4,2}*1152a, {6,6,6,2}*1152a, {6,12,2,2}*1152a, {6,12,2,2}*1152b, {12,6,2,2}*1152a
13-fold covers : {6,2,2,26}*1248, {6,2,26,2}*1248, {6,26,2,2}*1248, {78,2,2,2}*1248
14-fold covers : {12,2,2,14}*1344, {12,2,14,2}*1344, {12,14,2,2}*1344, {6,2,2,28}*1344, {6,2,28,2}*1344, {6,28,2,2}*1344a, {6,2,4,14}*1344, {6,2,14,4}*1344, {6,4,2,14}*1344a, {6,4,14,2}*1344, {6,14,2,4}*1344, {6,14,4,2}*1344, {84,2,2,2}*1344, {42,2,2,4}*1344, {42,2,4,2}*1344, {42,4,2,2}*1344a
15-fold covers : {18,2,2,10}*1440, {18,2,10,2}*1440, {18,10,2,2}*1440, {90,2,2,2}*1440, {6,2,6,10}*1440, {6,2,10,6}*1440, {6,6,2,10}*1440a, {6,6,2,10}*1440c, {6,6,10,2}*1440a, {6,6,10,2}*1440c, {6,10,2,6}*1440, {6,10,6,2}*1440, {6,30,2,2}*1440a, {6,2,2,30}*1440, {6,2,30,2}*1440, {6,30,2,2}*1440b, {30,2,2,6}*1440, {30,2,6,2}*1440, {30,6,2,2}*1440b, {30,6,2,2}*1440c
17-fold covers : {6,2,2,34}*1632, {6,2,34,2}*1632, {6,34,2,2}*1632, {102,2,2,2}*1632
18-fold covers : {108,2,2,2}*1728, {54,2,2,4}*1728, {54,2,4,2}*1728, {54,4,2,2}*1728a, {12,2,2,18}*1728, {12,2,18,2}*1728, {12,18,2,2}*1728a, {18,2,2,12}*1728, {18,2,12,2}*1728, {18,12,2,2}*1728a, {6,2,2,36}*1728, {6,2,36,2}*1728, {6,36,2,2}*1728a, {36,2,2,6}*1728, {36,2,6,2}*1728, {36,6,2,2}*1728a, {36,6,2,2}*1728b, {6,6,12,2}*1728a, {6,12,2,2}*1728b, {12,6,2,2}*1728a, {12,6,2,2}*1728b, {12,6,6,2}*1728a, {6,2,4,18}*1728a, {6,2,18,4}*1728a, {6,4,2,18}*1728a, {6,4,18,2}*1728, {6,18,2,4}*1728a, {6,18,4,2}*1728a, {18,2,4,6}*1728a, {18,2,6,4}*1728a, {18,4,2,6}*1728a, {18,4,6,2}*1728, {18,6,2,4}*1728a, {18,6,2,4}*1728b, {18,6,4,2}*1728a, {6,6,6,4}*1728a, {6,6,2,4}*1728b, {6,6,2,4}*1728c, {6,6,4,2}*1728b, {6,12,6,2}*1728a, {18,6,4,2}*1728b, {18,12,2,2}*1728b, {6,6,4,2}*1728c, {6,12,2,2}*1728c, {6,2,6,12}*1728a, {6,2,6,12}*1728b, {6,2,12,6}*1728a, {6,2,12,6}*1728b, {6,6,2,12}*1728a, {6,6,2,12}*1728c, {6,6,12,2}*1728b, {6,6,12,2}*1728c, {6,12,2,6}*1728a, {6,12,6,2}*1728b, {6,12,6,2}*1728d, {12,2,6,6}*1728a, {12,2,6,6}*1728b, {12,2,6,6}*1728c, {12,6,2,6}*1728a, {12,6,2,6}*1728b, {12,6,6,2}*1728b, {12,6,6,2}*1728c, {12,6,6,2}*1728d, {6,4,6,6}*1728a, {6,4,6,6}*1728b, {6,6,4,6}*1728a, {6,6,6,4}*1728d, {6,6,6,4}*1728e, {6,6,2,4}*1728d, {6,6,12,2}*1728e, {6,12,2,2}*1728g, {12,6,2,2}*1728g, {12,6,6,2}*1728e, {6,4,6,6}*1728c, {6,6,4,6}*1728c, {6,6,6,4}*1728g, {6,2,6,12}*1728c, {6,2,12,6}*1728c, {6,6,4,2}*1728h, {6,6,12,2}*1728f, {6,12,2,6}*1728c, {6,12,6,2}*1728f, {6,12,6,2}*1728g, {6,6,6,4}*1728i, {6,2,4,4}*1728, {6,2,4,6}*1728, {6,2,6,4}*1728, {6,4,2,2}*1728b, {6,4,4,2}*1728b, {6,4,6,2}*1728a, {6,6,4,2}*1728j, {6,6,4,2}*1728k, {12,4,2,2}*1728b, {12,6,2,2}*1728i
19-fold covers : {6,2,2,38}*1824, {6,2,38,2}*1824, {6,38,2,2}*1824, {114,2,2,2}*1824
20-fold covers : {30,2,4,4}*1920, {30,4,4,2}*1920, {60,4,2,2}*1920a, {6,4,4,10}*1920, {6,10,4,4}*1920, {12,4,2,10}*1920a, {12,4,10,2}*1920, {6,2,4,20}*1920, {6,2,20,4}*1920, {6,4,20,2}*1920, {6,20,4,2}*1920, {12,20,2,2}*1920, {30,4,2,4}*1920a, {60,2,2,4}*1920, {60,2,4,2}*1920, {6,4,10,4}*1920, {12,2,4,10}*1920, {12,2,10,4}*1920, {12,10,2,4}*1920, {6,4,2,20}*1920a, {6,20,2,4}*1920a, {12,10,4,2}*1920, {12,2,2,20}*1920, {12,2,20,2}*1920, {30,2,2,8}*1920, {30,2,8,2}*1920, {30,8,2,2}*1920, {120,2,2,2}*1920, {6,2,8,10}*1920, {6,2,10,8}*1920, {6,8,2,10}*1920, {6,8,10,2}*1920, {6,10,2,8}*1920, {6,10,8,2}*1920, {24,2,2,10}*1920, {24,2,10,2}*1920, {24,10,2,2}*1920, {6,2,2,40}*1920, {6,2,40,2}*1920, {6,40,2,2}*1920, {6,4,2,10}*1920, {6,4,10,2}*1920, {6,20,2,2}*1920a, {30,4,2,2}*1920
Permutation Representation (GAP) :
```s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (7,8);;
s3 := ( 9,10);;
s4 := (11,12);;
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*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, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope