# Polytope of Type {10,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,10}*500
if this polytope has a name.
Group : SmallGroup(500,27)
Rank : 3
Schlafli Type : {10,10}
Number of vertices, edges, etc : 25, 125, 25
Order of s0s1s2 : 5
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{10,10,2} of size 1000
Vertex Figure Of :
{2,10,10} of size 1000
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {10,10}*1000c
3-fold covers : {10,30}*1500e, {30,10}*1500e
4-fold covers : {10,20}*2000b, {20,10}*2000b
Permutation Representation (GAP) :
```s0 := ( 2, 5)( 3, 4)( 6,21)( 7,25)( 8,24)( 9,23)(10,22)(11,16)(12,20)(13,19)
(14,18)(15,17);;
s1 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(11,21)(12,22)(13,23)(14,24)(15,25);;
s2 := ( 2, 5)( 3, 4)( 6, 7)( 8,10)(11,13)(14,15)(16,19)(17,18)(21,25)(22,24);;
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*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope