# A projective configuration

The six vertices of a triangular prism, three midpoints of square faces of the prism, six planes through a vertex and the opposite prism edge, and three planes through the square prism faces, that I used last night to construct a symmetric representation of the associahedron, also form a projective configuration: there are nine points, each on five planes, and nine planes, each containing five points, so its Hilbert symbol is \( (9_5 9_5) \). I wonder whether it has a name.