1A prism connects two matching bases with side faces
A prism has two congruent polygon bases, one on top and one on the bottom, connected by rectangular side faces. If the base is an n-sided polygon, there are also n side faces.
Rectangular prism: 6 faces, 12 edges, 8 vertices
This is actually the exact same structure as the rectangular prism you already know!
2A pyramid gathers one base to a point at the top
A pyramid has just one base, and each side of that base connects through a triangular face up to a single point at the top (the apex). If the base is an n-sided polygon, there are also n triangular side faces.
Square pyramid: 5 faces, 8 edges, 5 vertices
Picture the pyramids of Egypt — that's exactly this shape.
3The number of sides (n) on the base tells you everything
When the base is an n-sided polygon, the number of faces, edges, and vertices in a prism or pyramid follows a fixed rule.
Prism: (n+2) faces, (3×n) edges, (2×n) vertices
Pyramid: (n+1) faces, (2×n) edges, (n+1) vertices
4Surprisingly, one rule always holds
(number of vertices) − (number of edges) + (number of faces) = 2
Whether it's a prism or a pyramid, and no matter how many sides the base has, this calculation always comes out to 2. It's called Euler's formula, and it's a wonderfully surprising rule about solid shapes.
Whether it's a prism or a pyramid, and no matter how many sides the base has, this calculation always comes out to 2. It's called Euler's formula, and it's a wonderfully surprising rule about solid shapes.
5Try this
- Increase n one at a time. Going from a triangular prism up to an octagonal prism, find the pattern in how the faces, edges, and vertices grow.
- Compare a prism and pyramid with the same n. Think about why the prism always has more of everything than the pyramid, even with the same n.
- Check Euler's formula yourself. Take the face, edge, and vertex numbers shown on screen and verify that they really do come out to 2.