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# Polytope of Type {3,5,2}

Atlas Canonical Name : {3,5,2}*120
if this polytope has a name.
Group : SmallGroup(120,35)
Rank : 4
Schlafli Type : {3,5,2}
Number of vertices, edges, etc : 6, 15, 10, 2
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,5,2,2} of size 240
{3,5,2,3} of size 360
{3,5,2,4} of size 480
{3,5,2,5} of size 600
{3,5,2,6} of size 720
{3,5,2,7} of size 840
{3,5,2,8} of size 960
{3,5,2,9} of size 1080
{3,5,2,10} of size 1200
{3,5,2,11} of size 1320
{3,5,2,12} of size 1440
{3,5,2,13} of size 1560
{3,5,2,14} of size 1680
{3,5,2,15} of size 1800
{3,5,2,16} of size 1920
Vertex Figure Of :
{2,3,5,2} of size 240
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,5,2}*240, {3,10,2}*240a, {3,10,2}*240b, {6,5,2}*240b, {6,5,2}*240c
4-fold covers : {3,10,4}*480, {3,10,2}*480, {6,5,2}*480b, {6,10,2}*480c, {6,10,2}*480d, {6,10,2}*480e, {6,10,2}*480f
6-fold covers : {3,10,6}*720, {3,10,2}*720, {3,15,2}*720, {6,15,2}*720
8-fold covers : {3,10,8}*960, {3,10,4}*960, {6,10,4}*960b, {6,10,4}*960c, {6,20,2}*960a, {6,20,2}*960b, {12,10,2}*960c, {12,10,2}*960d, {3,20,2}*960, {12,5,2}*960, {6,10,2}*960c
10-fold covers : {3,10,10}*1200, {6,5,2}*1200, {15,5,2}*1200, {15,10,2}*1200
12-fold covers : {3,10,12}*1440, {3,10,6}*1440, {6,10,6}*1440e, {6,10,6}*1440f, {3,10,2}*1440b, {3,30,2}*1440, {6,10,2}*1440b, {6,10,2}*1440c, {6,15,2}*1440c, {6,15,2}*1440d, {6,30,2}*1440a, {6,30,2}*1440b
14-fold covers : {3,10,14}*1680, {6,35,2}*1680, {21,10,2}*1680
16-fold covers : {3,10,16}*1920, {6,20,4}*1920d, {6,20,4}*1920e, {3,10,8}*1920, {6,10,8}*1920b, {6,10,8}*1920c, {6,40,2}*1920d, {6,40,2}*1920e, {24,10,2}*1920c, {24,10,2}*1920d, {6,10,4}*1920c, {6,20,2}*1920c, {12,10,2}*1920c, {3,20,4}*1920, {6,20,2}*1920e, {12,10,2}*1920e, {6,10,2}*1920b, {3,5,4}*1920b, {3,5,4}*1920c, {6,5,2}*1920
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(4,5);;
s2 := (2,4)(3,5);;
s3 := (6,7);;
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,
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2 ];;
poly := F / rels;;

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

```

to this polytope