Starting from the observation that for neighboring orders $p=2^{ n}-1, p'=2^{ n+1}-1 $ of the well-known Green's representations of parafermi algebra there exists a specifiable interordinal relationship, matrices with similar properties are constructed. They exhibit intrinsic Catalan structure and sine-like and cosine-like substructures, dubbed interordinal and intraordinal respectively, that seemingly have a bearing on Euclidean geometry and applications via Nebe kissing numbers.
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