Lesson 6: Polyhedra, Prisms, and Pyramids

Property

Every polyhedron is constructed from three basic parts:

• Faces: The flat polygonal surfaces of the solid.
• Edges: The straight line segments formed where two faces intersect.
• Vertices: The corner points where three or more edges meet.

Examples

• A cube has 6 faces (squares), 12 edges, and 8 vertices.
• A triangular prism has 5 faces total (2 triangular bases + 3 rectangular sides), 9 edges, and 6 vertices.
• A triangular pyramid has 4 faces (all triangles), 6 edges, and 4 vertices.

Explanation

To break down any 3D shape, just count its parts! Faces are the flat sides you can touch, edges are the straight lines you can trace with your finger, and vertices are the pointy corners. Counting these components is the first step to classifying any 3D figure.

Property

A prism has two parallel, congruent bases and rectangular lateral faces connecting the bases.
The total number of faces equals the number of sides of the base plus $2$.

Examples

Property

A pyramid is a polyhedron with one polygon base and triangular faces that meet at a single point called the apex. The faces that meet at the apex are called lateral faces, and the edges connecting the base to the apex are called lateral edges.

Examples

• A square pyramid has 1 square base, 4 triangular lateral faces, 5 vertices (including the apex), and 8 edges.
• A triangular pyramid (tetrahedron) has 1 triangular base, 3 triangular lateral faces, 4 vertices, and 6 edges.

Explanation

A pyramid is named for the shape of its single base. All other faces are triangles that connect the base to a common vertex called the apex. Understanding these components helps in classifying pyramids and analyzing their properties, such as surface area and volume.