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# Polytope of Type {10,4}

Atlas Canonical Name : {10,4}*200
if this polytope has a name.
Group : SmallGroup(200,43)
Rank : 3
Schlafli Type : {10,4}
Number of vertices, edges, etc : 25, 50, 10
Order of s0s1s2 : 4
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{10,4,2} of size 400
{10,4,4} of size 800
{10,4,6} of size 1200
{10,4,8} of size 1600
{10,4,10} of size 2000
Vertex Figure Of :
{2,10,4} of size 400
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,4}*400
3-fold covers : {10,12}*600
4-fold covers : {10,8}*800, {20,4}*800
5-fold covers : {10,4}*1000, {10,20}*1000a, {10,20}*1000b, {10,20}*1000c, {10,20}*1000d, {10,20}*1000e
6-fold covers : {30,4}*1200b, {10,12}*1200c
7-fold covers : {10,28}*1400
8-fold covers : {10,16}*1600, {20,4}*1600, {20,8}*1600a, {40,4}*1600a, {40,4}*1600b, {20,8}*1600b
9-fold covers : {10,36}*1800, {30,4}*1800
10-fold covers : {10,4}*2000a, {10,20}*2000d, {10,20}*2000e, {10,20}*2000f, {10,20}*2000g, {10,4}*2000b, {10,20}*2000i, {10,20}*2000j
Permutation Representation (GAP) :
```s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9);;
s1 := ( 6, 7)( 8,10);;
s2 := ( 1, 6)( 2, 8)( 3,10)( 4, 7)( 5, 9);;
poly := Group([s0,s1,s2]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope