Polyhedrons w. SketchUp
This page will suggest several ways it can be used to study polyhedrons. SketchUp enables students to create computer-generated polyhedrons in 3-dimensional space that they can manipulate and examine. The models can be copied, shared, interacted with, drawn to specifications, and modified for color, texture, and transparency. This will allow for a more thorough examination than with the familiar wooden blocks that are normally used.
To begin, students should learn how to construct prisms, cones pyramids, cylinders and spheres in SketchUp. Some are created easily and others are more difficult. The Polyhedron Models file included (link) illustrates how the basic solids are created in a step by step demonstration. Additionally, Platonic Solids, such as an icosahedron, are also possible in SketchUp.
In the spirit of E.A. Abbott’s novel, Flatland (link), another set of exercises allows students to explore the intersections of 2 and 3 dimensional objects using SketchUp. The students can do this by intersecting their polyhedra with planes or with each other, and examining their cross-sections. The models’ interiors can be examined by pulling the sections apart or by deleting one. The study of conic-sections, in particular, have been studied for thousands of years and have proven useful in astronomy (link).
Finally, surface area and volume formulas can be used with models created by the students or the teacher. Within SketchUp a polyhedron can be rotated, and inspected for its Euler characteristics (X= V - F + E) by counting edges, faces, and vertices. Related formulas, such as the volume of a cone and cylinder, can also be investigated by intersecting models.
A free version of SketchUp is available for download from Google @ http://sketchup.google.com/download.html. Once students have the program, they can use SketchUp without an Internet connection but the most useful help guides are online.
Getting started will require some instruction and practice with the multiple tools offered. Some polyhedron example files are included below for download. Links to Help guides and tutorials are available under the Help menu in SketchUp, as well as on the Resources page of this site.
Note: The primary download is a tutorial for building polyhedrons in SketchUp; it comes in the form a SketchUp .skp file. There are additional SketchUp files of polyhedrons included in the Teacher Downloads. You may want to use some of these as display models for your classroom instruction throughout the year.