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    Simplex

    Alternate name

    hypertetrahedron

    Combinatorial properties

    vertices | n + 1 edges | 1/2 n (n + 1) = 0.5 n (n + 1) faces | 1/6 (n - 1) n (n + 1)≈0.166667 (n - 1) n (n + 1) cells | n + 1 (assuming embedding dimension n)

    Properties

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

    Skeleton graph

    (n + 1)-complete graph

    Dual polytope

    n-simplex (polytope in n-dimensional space)

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