# Polytope of Type {5,2,10}

Atlas Canonical Name : {5,2,10}*200
if this polytope has a name.
Group : SmallGroup(200,49)
Rank : 4
Schlafli Type : {5,2,10}
Number of vertices, edges, etc : 5, 5, 10, 10
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,2,10,2} of size 400
{5,2,10,4} of size 800
{5,2,10,5} of size 1000
{5,2,10,3} of size 1200
{5,2,10,3} of size 1200
{5,2,10,5} of size 1200
{5,2,10,5} of size 1200
{5,2,10,6} of size 1200
{5,2,10,8} of size 1600
{5,2,10,4} of size 2000
{5,2,10,10} of size 2000
{5,2,10,10} of size 2000
{5,2,10,10} of size 2000
Vertex Figure Of :
{2,5,2,10} of size 400
{3,5,2,10} of size 1200
{5,5,2,10} of size 1200
{10,5,2,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,2,5}*100
5-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,2,20}*400, {10,2,10}*400
3-fold covers : {5,2,30}*600, {15,2,10}*600
4-fold covers : {5,2,40}*800, {10,2,20}*800, {20,2,10}*800, {10,4,10}*800
5-fold covers : {5,2,50}*1000, {25,2,10}*1000, {5,10,10}*1000a, {5,10,10}*1000b
6-fold covers : {15,2,20}*1200, {5,2,60}*1200, {10,6,10}*1200, {10,2,30}*1200, {30,2,10}*1200
7-fold covers : {5,2,70}*1400, {35,2,10}*1400
8-fold covers : {5,2,80}*1600, {20,2,20}*1600, {10,4,20}*1600, {20,4,10}*1600, {10,2,40}*1600, {40,2,10}*1600, {10,8,10}*1600
9-fold covers : {5,2,90}*1800, {45,2,10}*1800, {15,6,10}*1800, {15,2,30}*1800
10-fold covers : {25,2,20}*2000, {5,2,100}*2000, {5,10,20}*2000a, {10,2,50}*2000, {50,2,10}*2000, {10,10,10}*2000a, {5,10,20}*2000b, {10,10,10}*2000b, {10,10,10}*2000c, {10,10,10}*2000g
Permutation Representation (GAP) :
```s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 8, 9)(10,11)(12,13)(14,15);;
s3 := ( 6,10)( 7, 8)( 9,14)(11,12)(13,15);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(15)!(2,3)(4,5);
s1 := Sym(15)!(1,2)(3,4);
s2 := Sym(15)!( 8, 9)(10,11)(12,13)(14,15);
s3 := Sym(15)!( 6,10)( 7, 8)( 9,14)(11,12)(13,15);
poly := sub<Sym(15)|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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```

to this polytope