Back

Answers

Do you think there are an infinite or finite number of semi-regular convex polyhedra? Play around with the polydrons to see what sort of semi-regular polyhedra you can make.

One way to get a polyhedron satisfying these requirements is to take two copies of a regular polygon and join them together with squares as in the picture http://amath.colorado.edu/staff/fast/Polyhedra/GIFs/prism7.gif

In this picture the two polygons were heptagons, but we could have used any regular polygon for the top and the bottom. These semi-regular polyhedra are called prisms and form an infinite family.

There is another very similar infinite family of semi-regular polyhedra, the anti-prisms, which are formed by joining two copies of a regular polygon with triangles as in http://home.att.net/~numericana/answer/antiprism6.gif

So, there are an infinite number of semi-regular polyhedra. However, if we eliminate these two infinite families from consideration, there are only a finite number.