Consider a cube, which has eight vertices, or corners. Suppose I assign a prime number to each vertex. A “face sum” is the value I get when I add up all four prime numbers on one of the six faces.

This 6 c m × 6 c m × 6 c m cube has been drawn using the dots as guides. The vertical lines are always vertical, but the horizontal lines are drawn at an angle, when drawn on isometric dotted paper.

3-dimensional shapes have faces, edges and vertices. Volume is the space contained within a 3D shape. Surface area is the sum of the area of each face. 3D shapes can be viewed from different points.