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# Polytope of Type {4,3,2}

Atlas Canonical Name : {4,3,2}*48
if this polytope has a name.
Group : SmallGroup(48,48)
Rank : 4
Schlafli Type : {4,3,2}
Number of vertices, edges, etc : 4, 6, 3, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Locally Projective
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,3,2,2} of size 96
{4,3,2,3} of size 144
{4,3,2,4} of size 192
{4,3,2,5} of size 240
{4,3,2,6} of size 288
{4,3,2,7} of size 336
{4,3,2,8} of size 384
{4,3,2,9} of size 432
{4,3,2,10} of size 480
{4,3,2,11} of size 528
{4,3,2,12} of size 576
{4,3,2,13} of size 624
{4,3,2,14} of size 672
{4,3,2,15} of size 720
{4,3,2,16} of size 768
{4,3,2,17} of size 816
{4,3,2,18} of size 864
{4,3,2,19} of size 912
{4,3,2,20} of size 960
{4,3,2,21} of size 1008
{4,3,2,22} of size 1056
{4,3,2,23} of size 1104
{4,3,2,24} of size 1152
{4,3,2,25} of size 1200
{4,3,2,26} of size 1248
{4,3,2,27} of size 1296
{4,3,2,28} of size 1344
{4,3,2,29} of size 1392
{4,3,2,30} of size 1440
{4,3,2,31} of size 1488
{4,3,2,33} of size 1584
{4,3,2,34} of size 1632
{4,3,2,35} of size 1680
{4,3,2,36} of size 1728
{4,3,2,37} of size 1776
{4,3,2,38} of size 1824
{4,3,2,39} of size 1872
{4,3,2,40} of size 1920
{4,3,2,41} of size 1968
Vertex Figure Of :
{2,4,3,2} of size 96
{4,4,3,2} of size 384
{4,4,3,2} of size 768
{6,4,3,2} of size 1440
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
3-fold covers : {4,9,2}*144, {4,3,6}*144
4-fold covers : {4,12,2}*192b, {4,12,2}*192c, {4,6,4}*192c, {8,3,2}*192, {4,6,2}*192, {4,3,4}*192a
5-fold covers : {4,15,2}*240
6-fold covers : {4,9,2}*288, {4,18,2}*288b, {4,18,2}*288c, {4,3,6}*288, {4,6,6}*288d, {4,6,6}*288e, {4,6,6}*288f, {12,3,2}*288, {12,6,2}*288d
7-fold covers : {4,21,2}*336
8-fold covers : {4,12,4}*384d, {4,12,4}*384e, {4,6,2}*384a, {8,3,2}*384, {8,6,2}*384a, {4,24,2}*384c, {4,24,2}*384d, {4,6,8}*384b, {4,12,2}*384b, {4,6,4}*384b, {4,6,2}*384b, {4,12,2}*384c, {8,6,2}*384b, {8,6,2}*384c, {4,3,8}*384, {4,3,4}*384, {4,6,4}*384c, {4,6,4}*384f
9-fold covers : {4,27,2}*432, {4,9,6}*432, {4,3,6}*432
10-fold covers : {4,6,10}*480b, {20,6,2}*480b, {4,15,2}*480, {4,30,2}*480b, {4,30,2}*480c
11-fold covers : {4,33,2}*528
12-fold covers : {4,36,2}*576b, {4,36,2}*576c, {4,18,4}*576c, {8,9,2}*576, {4,18,2}*576, {4,9,4}*576a, {4,12,6}*576d, {4,12,6}*576e, {4,12,6}*576f, {4,12,6}*576g, {4,6,12}*576d, {24,3,2}*576, {8,3,6}*576, {4,6,12}*576e, {4,3,6}*576, {4,6,6}*576a, {4,6,6}*576b, {12,6,2}*576a, {12,6,2}*576b, {4,3,12}*576
13-fold covers : {4,39,2}*624
14-fold covers : {4,6,14}*672b, {28,6,2}*672b, {4,21,2}*672, {4,42,2}*672b, {4,42,2}*672c
15-fold covers : {4,45,2}*720, {4,15,6}*720
16-fold covers : {8,3,2}*768, {8,6,2}*768a, {8,12,2}*768c, {8,12,2}*768d, {4,12,2}*768b, {4,12,2}*768c, {4,6,4}*768b, {4,24,4}*768g, {4,24,4}*768h, {4,12,4}*768d, {4,24,4}*768k, {4,24,4}*768l, {4,12,8}*768c, {4,12,8}*768d, {4,12,8}*768e, {8,6,2}*768b, {8,6,2}*768c, {4,48,2}*768c, {4,48,2}*768d, {4,6,16}*768b, {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, {4,3,8}*768a, {4,6,4}*768g, {4,12,4}*768i, {4,12,4}*768l, {4,12,4}*768m, {4,12,4}*768n, {4,3,8}*768b, {4,6,8}*768e, {4,6,8}*768f, {8,3,4}*768b, {4,6,8}*768g, {4,3,8}*768c, {4,6,8}*768h, {8,3,4}*768c, {4,3,4}*768, {4,6,4}*768i, {4,6,4}*768j, {4,6,4}*768l
17-fold covers : {4,51,2}*816
18-fold covers : {4,27,2}*864, {4,54,2}*864b, {4,54,2}*864c, {4,6,18}*864c, {36,6,2}*864c, {4,9,6}*864, {4,18,6}*864c, {4,18,6}*864d, {4,18,6}*864e, {12,9,2}*864, {12,18,2}*864c, {4,3,6}*864, {4,6,6}*864d, {4,6,6}*864e, {4,6,6}*864f, {12,3,2}*864, {12,6,2}*864d, {4,6,6}*864i, {12,3,6}*864, {12,6,6}*864h
19-fold covers : {4,57,2}*912
20-fold covers : {4,12,10}*960b, {4,12,10}*960c, {4,6,20}*960b, {4,60,2}*960b, {4,60,2}*960c, {4,30,4}*960c, {8,15,2}*960, {4,6,10}*960e, {20,6,2}*960c, {4,30,2}*960, {4,15,4}*960a
21-fold covers : {4,63,2}*1008, {4,21,6}*1008
22-fold covers : {4,6,22}*1056b, {44,6,2}*1056b, {4,33,2}*1056, {4,66,2}*1056b, {4,66,2}*1056c
23-fold covers : {4,69,2}*1104
24-fold covers : {4,36,4}*1152d, {4,36,4}*1152e, {4,18,2}*1152a, {8,9,2}*1152, {8,18,2}*1152a, {4,72,2}*1152c, {4,72,2}*1152d, {4,18,8}*1152b, {4,36,2}*1152b, {4,18,4}*1152b, {4,18,2}*1152b, {4,36,2}*1152c, {8,18,2}*1152b, {8,18,2}*1152c, {4,9,8}*1152, {24,3,2}*1152, {24,6,2}*1152a, {4,6,6}*1152a, {4,6,6}*1152b, {8,3,6}*1152, {8,6,6}*1152a, {4,24,6}*1152g, {4,24,6}*1152h, {4,24,6}*1152i, {4,24,6}*1152j, {4,6,24}*1152d, {4,12,12}*1152d, {4,12,12}*1152e, {4,12,12}*1152f, {4,12,12}*1152g, {4,6,24}*1152e, {4,9,4}*1152, {4,18,4}*1152c, {4,18,4}*1152f, {4,3,12}*1152a, {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, {4,3,24}*1152, {4,3,6}*1152b, {4,6,6}*1152g, {4,6,6}*1152h, {4,12,6}*1152k, {12,3,2}*1152, {12,12,2}*1152l, {4,3,12}*1152b, {4,6,12}*1152e, {4,6,12}*1152f, {4,6,12}*1152h, {12,3,4}*1152b, {12,6,4}*1152e
25-fold covers : {4,75,2}*1200, {4,15,10}*1200, {4,3,10}*1200
26-fold covers : {4,6,26}*1248b, {52,6,2}*1248b, {4,39,2}*1248, {4,78,2}*1248b, {4,78,2}*1248c
27-fold covers : {4,81,2}*1296, {4,27,6}*1296, {4,9,18}*1296, {4,3,18}*1296, {4,3,6}*1296a, {4,9,6}*1296a, {4,9,6}*1296b, {4,9,6}*1296c, {4,9,6}*1296d, {4,9,2}*1296, {12,3,2}*1296, {12,9,2}*1296a, {12,9,2}*1296b
28-fold covers : {4,12,14}*1344b, {4,12,14}*1344c, {4,6,28}*1344b, {4,84,2}*1344b, {4,84,2}*1344c, {4,42,4}*1344c, {8,21,2}*1344, {4,6,14}*1344, {28,6,2}*1344, {4,42,2}*1344, {4,21,4}*1344a
29-fold covers : {4,87,2}*1392
30-fold covers : {4,18,10}*1440b, {20,18,2}*1440b, {4,45,2}*1440, {4,90,2}*1440b, {4,90,2}*1440c, {4,6,30}*1440d, {20,6,6}*1440d, {4,15,6}*1440b, {4,30,6}*1440d, {4,30,6}*1440e, {4,30,6}*1440f, {12,15,2}*1440, {12,30,2}*1440d, {4,6,30}*1440e, {60,6,2}*1440d
31-fold covers : {4,93,2}*1488
33-fold covers : {4,99,2}*1584, {4,33,6}*1584
34-fold covers : {4,6,34}*1632b, {68,6,2}*1632b, {4,51,2}*1632, {4,102,2}*1632b, {4,102,2}*1632c
35-fold covers : {4,105,2}*1680
36-fold covers : {4,108,2}*1728b, {4,108,2}*1728c, {4,54,4}*1728c, {8,27,2}*1728, {4,54,2}*1728, {4,27,4}*1728a, {4,12,18}*1728c, {4,12,18}*1728d, {4,6,36}*1728c, {4,36,6}*1728c, {4,36,6}*1728d, {4,36,6}*1728e, {4,36,6}*1728f, {4,18,12}*1728c, {4,12,6}*1728d, {4,12,6}*1728e, {4,12,6}*1728f, {4,12,6}*1728g, {4,6,12}*1728d, {24,9,2}*1728, {24,3,2}*1728, {8,9,6}*1728, {8,3,6}*1728, {4,18,12}*1728d, {4,6,12}*1728e, {4,9,6}*1728, {4,3,6}*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, {4,9,12}*1728, {4,3,12}*1728, {24,3,6}*1728, {4,12,6}*1728l, {4,12,6}*1728m, {4,6,12}*1728j, {4,6,4}*1728f, {4,12,4}*1728f, {4,12,6}*1728r, {12,12,2}*1728o, {4,6,6}*1728c, {12,6,6}*1728a, {12,6,6}*1728b, {12,6,6}*1728c, {12,6,6}*1728d, {12,6,2}*1728c
37-fold covers : {4,111,2}*1776
38-fold covers : {4,6,38}*1824b, {76,6,2}*1824b, {4,57,2}*1824, {4,114,2}*1824b, {4,114,2}*1824c
39-fold covers : {4,117,2}*1872, {4,39,6}*1872
40-fold covers : {40,6,2}*1920a, {4,6,10}*1920a, {4,24,10}*1920c, {4,24,10}*1920d, {4,6,40}*1920b, {4,12,20}*1920b, {4,12,20}*1920c, {4,60,4}*1920d, {4,60,4}*1920e, {4,30,2}*1920a, {8,15,2}*1920a, {8,30,2}*1920a, {4,120,2}*1920c, {4,120,2}*1920d, {4,30,8}*1920b, {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, {4,15,8}*1920, {4,6,20}*1920c, {20,6,4}*1920c, {4,15,4}*1920c, {4,30,4}*1920c, {4,30,4}*1920f
41-fold covers : {4,123,2}*1968
Permutation Representation (GAP) :
```s0 := (1,2)(3,4);;
s1 := (2,3);;
s2 := (3,4);;
s3 := (5,6);;
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,
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```

to this polytope