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# Polytope of Type {3,4,2,5}

Atlas Canonical Name : {3,4,2,5}*240
if this polytope has a name.
Group : SmallGroup(240,194)
Rank : 5
Schlafli Type : {3,4,2,5}
Number of vertices, edges, etc : 3, 6, 4, 5, 5
Order of s0s1s2s3s4 : 15
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,4,2,5,2} of size 480
{3,4,2,5,3} of size 1440
{3,4,2,5,5} of size 1440
Vertex Figure Of :
{2,3,4,2,5} of size 480
{4,3,4,2,5} of size 960
{6,3,4,2,5} of size 1440
{4,3,4,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,4,2,5}*480, {3,4,2,10}*480, {6,4,2,5}*480b, {6,4,2,5}*480c
3-fold covers : {9,4,2,5}*720, {3,4,2,15}*720
4-fold covers : {12,4,2,5}*960b, {12,4,2,5}*960c, {3,4,2,20}*960, {3,8,2,5}*960, {3,4,2,10}*960, {6,4,2,5}*960, {6,4,2,10}*960b, {6,4,2,10}*960c
5-fold covers : {3,4,2,25}*1200, {15,4,2,5}*1200
6-fold covers : {9,4,2,5}*1440, {9,4,2,10}*1440, {18,4,2,5}*1440b, {18,4,2,5}*1440c, {3,12,2,5}*1440, {6,12,2,5}*1440d, {3,4,2,15}*1440, {3,4,2,30}*1440, {6,4,2,15}*1440b, {6,4,2,15}*1440c
7-fold covers : {21,4,2,5}*1680, {3,4,2,35}*1680
8-fold covers : {3,4,4,10}*1920a, {6,4,2,5}*1920a, {3,8,2,5}*1920, {6,8,2,5}*1920a, {24,4,2,5}*1920c, {24,4,2,5}*1920d, {3,4,2,40}*1920, {12,4,2,5}*1920b, {12,4,2,10}*1920b, {12,4,2,10}*1920c, {3,4,2,20}*1920, {6,4,2,20}*1920b, {6,4,2,20}*1920c, {3,4,4,10}*1920b, {6,4,2,5}*1920b, {12,4,2,5}*1920c, {3,8,2,10}*1920, {6,8,2,5}*1920b, {6,8,2,5}*1920c, {6,4,2,10}*1920
Permutation Representation (GAP) :
```s0 := (3,4);;
s1 := (2,3);;
s2 := (1,2)(3,4);;
s3 := (6,7)(8,9);;
s4 := (5,6)(7,8);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s2*s1*s0*s2*s1*s0*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

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

```

to this polytope