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Cross Polytope

Alternate name

Combinatorial properties

vertices | 2 n
edges | 2 (n - 1) n
faces | 4/3 (n - 2) (n - 1) n≈1.33333 (n - 2) (n - 1) n
cells | 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)