In one of his papers [2], A. Neumaier constructed a rank 4 incidence geometry on which the alternating group of degree 8 acts flag-transitively. This geometry is quite important since its point residue is the famous. A(7)-geometry which is known to be the only flag-transitive locally classical C-3-geometry which is not a polar space (sce [1]). By counting chambers, we prove that the A(8)-geometry has 70 planes. This can be found in a paper of Pasini's [4] without proof, but Neumaier's original paper only mentions 35 planes. (C) 2001 Academic Press. [References: 5]
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