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

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

n-hypercube graph

n-cross polytope (polytope in n-dimensional space)