A Hands-On Approach to Finding Plantonic Volumes

In my last column, I showed how to find the volume of anti-prisms. After finishing it, it occurred to me that you never see in any textbooks mention of how to find the volumes of icosahedra and dodecahedra.

This Geometer's Corner is about how you can use a set of manipulatives, Zometools, to build models of each that suggest a way to find their volumes and surface areas. We will be doing a lot of work with regular pyramids, pyramids with bases that are regular polygons and lateral faces that are isosceles triangles.

I have created a spreadsheet that does all the calculations and will use it later in the article.