On the uniqueness of a certain thin near octagon (or partial 2-geometry, or parallelism) derived from the binary Golay code

The question of the uniqueness of a certain combinatorial structure has arisen in three contexts: a) is the regular near octagon with parameters(s,t_{2},t_{3},t)=(1, 1,2,23)unique [5]? b) is the partial2-geometry with nexus three and blocksize24unique [2]? c) is there a unique graph such that it is the graph of a parallelism ofleft(^{24}_{4}right)with respect to any [1]? We observe that these questions are equivalent and give an affirmative answer. In fact, we prove a more general theorem, showing the truth of a conjecture by Cameron.