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# Polytope of Type {4,10}

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

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

```
References : None.
to this polytope