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For a pyramid to be "half an octahedron", its height must be the width divided by sqrt(2). Examination of the List of Egyptian pyramids shows that this is not the case. E.g., Sneferu: 220/(105*sqrt(2)) = 1.481557 Khufu: 230.3/(146.6*sqrt(2)) = 1.110823 Menkaure: 103.4/(65.5*sqrt(2)) = 1.116257 i.e., they are flatter than "half an octahedron".

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