**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” ¨.