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# Polytope of Type {10,5,2}

Atlas Canonical Name : {10,5,2}*200
if this polytope has a name.
Group : SmallGroup(200,49)
Rank : 4
Schlafli Type : {10,5,2}
Number of vertices, edges, etc : 10, 25, 5, 2
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{10,5,2,2} of size 400
{10,5,2,3} of size 600
{10,5,2,4} of size 800
{10,5,2,5} of size 1000
{10,5,2,6} of size 1200
{10,5,2,7} of size 1400
{10,5,2,8} of size 1600
{10,5,2,9} of size 1800
{10,5,2,10} of size 2000
Vertex Figure Of :
{2,10,5,2} of size 400
{4,10,5,2} of size 800
{5,10,5,2} of size 1000
{6,10,5,2} of size 1200
{8,10,5,2} of size 1600
{10,10,5,2} of size 2000
{10,10,5,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
5-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,10,2}*400b
3-fold covers : {10,15,2}*600
4-fold covers : {10,20,2}*800b, {10,10,4}*800b, {20,10,2}*800c
5-fold covers : {10,25,2}*1000, {10,5,2}*1000, {10,5,10}*1000
6-fold covers : {10,10,6}*1200b, {30,10,2}*1200a, {10,30,2}*1200c
7-fold covers : {10,35,2}*1400
8-fold covers : {10,20,4}*1600b, {10,40,2}*1600b, {10,10,8}*1600b, {20,20,2}*1600b, {20,10,4}*1600c, {40,10,2}*1600c
9-fold covers : {10,45,2}*1800, {10,15,6}*1800, {30,15,2}*1800
10-fold covers : {10,50,2}*2000b, {10,10,2}*2000b, {10,10,10}*2000d, {10,10,10}*2000f, {10,10,2}*2000d
Permutation Representation (GAP) :
```s0 := ( 4, 5)( 7, 8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25);;
s1 := ( 1, 4)( 2,10)( 3, 7)( 5,12)( 6,18)( 8,20)( 9,14)(11,16)(15,24)(17,21)
(19,22)(23,25);;
s2 := ( 1, 2)( 3, 6)( 4, 8)( 5, 7)(10,15)(11,14)(12,17)(13,16)(18,19)(20,23)
(21,22)(24,25);;
s3 := (26,27);;
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,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(27)!( 4, 5)( 7, 8)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)
(24,25);
s1 := Sym(27)!( 1, 4)( 2,10)( 3, 7)( 5,12)( 6,18)( 8,20)( 9,14)(11,16)(15,24)
(17,21)(19,22)(23,25);
s2 := Sym(27)!( 1, 2)( 3, 6)( 4, 8)( 5, 7)(10,15)(11,14)(12,17)(13,16)(18,19)
(20,23)(21,22)(24,25);
s3 := Sym(27)!(26,27);
poly := sub<Sym(27)|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, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

```

to this polytope