The last subconstituent of the Hemmeter graph

We prove that when q is any odd prime power, the distance-2 graph on the set of vertices at maximal distance D   from any fixed vertex of the Hemmeter graph HemD(q)HemD(q) is isomorphic to the graph QuadD-1(q)QuadD-1(q) of quadratic forms on FqD-1.