It Is 1727 and Leonhard Euler Is Pacing up and Down His Room

It is 1727 and Leonhard Euler is pacing up and down his room.

He cannot sleep, he dare not sleep! He cannot stop dreaming about crystal asteroids bombarding the earth.

He knows that these solid shapes are not random, but built to a rule linking the number of sides, faces and edges.

If only he could solve this problem then he would be able to sleep.

Dr. Who must travel back to 1727 to help Euler, go with him and solve the problem yourselves.

Look at this cube.

It has 6 faces.

It has 12 edges.

It has 8 vertices.

1.  Close your eyes and imagine a cuboid. How many faces does it have? How many edges? How many vertices? Open your eyes and write down your answers.

2.  Close your eyes and imagine a triangular prism. How many faces does it have? How many edges? How many vertices? Open your eyes and write down your answers.

3.  Close your eyes and imagine a square based pyramid. How many faces does it have? How many edges? How many vertices? Open your eyes and write down your answers.

4.  Close your eyes and imagine the same square based pyramid. It is standing on its square base. You take a sharp knife and slice off the top. Look at the piece that is left standing. How many faces does it have? How many edges? How many vertices? Open your eyes and write down your answers,

5.  Close your eyes and imagine two identical square based pyramids. You pick them up and join them sticking their square bases together. Look at the new shape you have made. How many faces does it have? How many edges? How many vertices? Open your eyes and write

down your answers.

Look at your results. What do you notice? Write down what you think the connection is.