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# Polytope of Type {2,5,3}

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

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

```

to this polytope