What is the sum of the vertices and faces in a triangular pyramid?

A triangular pyramid (also known as a tetrahedron) has a triangular base and three triangular faces that meet at a single point (apex).
It has 3 vertices on its base and 1 vertex at the apex.

$$\text{Number of vertices (V)} = 3 + 1 = 4$$

A triangular pyramid has 1 triangular base face and 3 triangular side faces.

$$\text{Number of faces (F)} = 1 + 3 = 4$$

$$\text{Sum} = \text{V} + \text{F} = 4 + 4 = 8$$

The sum of the vertices and faces in a triangular pyramid is 8.