hypertetrahedron

vertex count | n + 1 edge count | 1/2 n (n + 1) = 0.5 n (n + 1) face count | 1/6 (n - 1) n (n + 1)≈0.166667 (n - 1) n (n + 1) cell count | n + 1 (assuming embedding dimension n)

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)

(n + 1)-complete graph

n-simplex (polytope in n-dimensional space)