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# Polytope of Type {2,10,5}

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

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

```

to this polytope