Problem 8

In geometry, a net is a diagram in a two dimensional plane that shows the edges of a three dimensional polyhedron. For example, the net below is for a cube.

Describe and sketch the polyhedron with the following net:

[Problem submitted by Donald Hentschel, LACC Professor of Mathematics.]

Solution for Problem 8:

Once “folded” into a three-dimensional figure, this net will produce a polyhedron with eight triangular sides. This is known as an octahedron. The dashed edges in the diagram below indicate they are hidden lines an observer would not actually see.

Note: Natural diamonds often form in this shape before they are cut. That is why playing cards that have a simplified version of this figure are called “diamonds” ¨.