Construct prisms & pyramids
Theory
Build a prism from two identical ends and rectangles, and a pyramid from one base and triangles. A skeleton model uses one straw per edge and one join per vertex.
A prism has two identical ends, called its cross-section, joined by rectangles. It is named after the shape of its ends, so a triangular prism has triangular ends.
A pyramid has one base and triangular faces that all meet at a single point called the apex. It is named after its base, so a square pyramid has a square base.
A face is a flat surface, an edge is where two faces meet, and a vertex is a corner. A skeleton model uses one straw for every edge and one join for every vertex.
These counts are worth knowing by heart, because they give the pieces, straws and joins needed to build each shape.
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Cube | \(6\) | \(12\) | \(8\) |
| Rectangular prism | \(6\) | \(12\) | \(8\) |
| Triangular prism | \(5\) | \(9\) | \(6\) |
| Square pyramid | \(5\) | \(8\) | \(5\) |
For a skeleton model, the number of straws matches the edges and the number of joins matches the vertices.
Working out the pieces
- Name the solid by its ends (prism) or its base (pyramid).
- Count the flat faces: two ends plus one rectangle per side for a prism; one base plus one triangle per side for a pyramid.
- Count the edges for the straws in a skeleton model.
- Count the vertices for the joins in a skeleton model.
Two triangular ends and three rectangles.
| \(2 + 3\) | \(=\) | \(5\) |
It has \(5\) faces.
One square base and one triangle for each of its four sides.
| \(1 + 4\) | \(=\) | \(5\) |
\(1\) square and \(4\) triangles.
Top and bottom, four sides; edges in three groups of four; corners top and bottom.
| faces, edges, vertices | \(=\) | \(6,\ 12,\ 8\) |
Straws match the edges, joins match the vertices.
| straws, joins | \(=\) | \(9,\ 6\) |
Common pitfalls
Frequently asked questions
How many faces does a triangular prism have?
Five. There are two triangular ends and three rectangles joining them, so \(2 + 3 = 5\) faces.
What pieces make a square pyramid?
One square base and four triangles, one leaning in from each side of the square to the apex. That is \(1 + 4 = 5\) faces.
How many straws does a skeleton cube need?
Twelve, one for each edge: four around the top, four around the bottom and four upright straws joining them.
What is the difference between a face, an edge and a vertex?
A face is a flat surface, an edge is the line where two faces meet, and a vertex is a corner where edges meet.
How is a prism named?
A prism is named after its cross-section, the shape of its two identical ends. Triangular ends give a triangular prism.