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# Polytope of Type {2,3,3}

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

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

```

to this polytope