hyperoctahedron

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)

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)

n-cross polytope graph

n-cube (polytope in n-dimensional space)