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    Cross Polytope

    Alternate name
    Combinatorial properties

    vertex count | 2 n
edge count | 2 (n - 1) n
face count | 4/3 (n - 2) (n - 1) n≈1.33333 (n - 2) (n - 1) n
cell count | 2^n
(assuming embedding dimension n)

    Properties

    content | (sqrt(2^n) s^n)/(n!)
hyper-surface area | (sqrt(2^(n + 1) n) s^(n - 1))/((n - 1)!)
(assuming embedding dimension n and edge length s)

    Skeleton graph

    n-cross polytope graph

    Dual polytope

    n-cube (polytope in n-dimensional space)

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