Changed. Thanks

I agree. It's also mentioned in the the first sentence on Wikipedia:

Rack (billiards)
A rack (sometimes called a triangle) is a piece of equipment that is used to place billiard balls in their starting positions at the beginning of a pocket billiards game.

Minor niggle but threw me a little when I first started thinking about the solution:
Technically speaking a pyramid is a 3D structure, so a more complicated calculation by far (layers of decreasing numbers of balls on top of larger base layers in the shape of a pyramid), whereas the shape of the billiards is only 2D and should be refered to as a triangle.