In elementary geometry, a face is a polygon on the boundary of a polyhedron. Other names for a polygonal face include side of a polyhedron, and tile of a Euclidean plane tessellation. For example, any of the six squares that bound a cube is a face of the cube.

pyramid

a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex (called the vertex of the pyramid).

6 lateral faces

In solid geometry, a vertex is the point where three or more edges meet. In everyday terms, a vertex of a solid shape is a ‘corner’.

Polyhedrons are solids with flat faces. Any 3-dimensional solid is a polyhedron if all of its sides are flat. Examples of real-world polyhedrons include soccer balls, prisms, bricks, houses, and pyramids. All of these shapes have flat sides.

A vertex is a corner where edges meet. The plural is vertices. For example a cube has eight vertices, a cone has one vertex and a sphere has none.

octahedron

Vertices, edges and faces