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# Chiral Polytope of Type {9,18}

Regular Cover :{9,18}*972a with group SmallGroup(972,99) = (C3 x C9) ⋊ (D9 x C2)of order 972
Rank : 3
Schlafli Type : {9,18}
Rotation Group : SmallGroup(162,6) = (C9 ⋊ C9) ⋊ C2 of order 162
Number of vertices, edges, etc : 9, 81, 18
If Aut({9,18}*972a)=<s0, s1, s2>, then this chiral polytope is ({9,18}*972a)/N, where
N=<s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 3
Facet : (Regular) 9-gon
Vertex Figure : (Regular) 18-gon
Finitely Presented Group Representation of the Rotation Group(GAP) :
```F := FreeGroup("sig1","sig2");;
sig1 := F.1;;  sig2 := F.2;;
rels := [ sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1,
sig1*sig1*sig1*sig1*sig2^-1*sig2^-1*sig2^-1*sig1*sig2^-1 ];;
rotpoly := F / rels;;

```
Finitely Presented Group Representation of the Rotation Group (Magma) :

```rotpoly<sig1,sig2> := Group< sig1,sig2 | sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1*sig1,
sig1*sig1*sig1*sig1*sig2^-1*sig2^-1*sig2^-1*sig1*sig2^-1 >;

```