Two-dimensional figures and three-dimensional solids share some features, but they also have differences. The similarities and differences between two-dimensional figures and three-dimensional solids can be used to describe three-dimensional solids in terms of the shapes of their faces and cross-sections, their edges, which can be curved or straight, and their vertices, which are pointed.

For example, both a square and a cube have a square component, as the base and faces of a cube are squares. However, the square is a flat, two-dimensional figure measured by area, while a cube is a three-dimensional solid that has surface area and volume. In a square, edges are the sides, and vertices are where the two sides meet. In a cube, edges are where two faces meet, and vertices are where three faces meet. A square has 4 straight edges and 4 vertices, while a cube has 12 straight edges and 8 vertices. Furthermore, a cube can be sliced to reveal two-dimensional cross-sections, which could take the shape of a square or several other shapes.