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# Polytope of Type {5,10,2}

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

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

```

to this polytope