Polyhedra Workshops for Teachers

Workshop 1 should be completed first. This will ensure that all participants have a working knowledge of basic vocabulary and concepts relating to polyhedra. It is the only prerequisite for most other workshops.

A minimum of 90 minutes should be allowed for each workshop to get a feel for the topic. There is no substitute for hands-on work, and this takes time!

As curricula differ by country, workshops may be modified to address particular issues relevant to national or state curricula. Additional workshops maybe created to address specific needs or interests.

Note: Best viewed in Firefox.

Construction of the Platonic solids. Build the Platonic solids and deltahedra using plastic snap-together pieces or paper nets. Discover geometric proofs that all have been found. Link to algebra by applying Euler's formula and Descartes' rule of deficiency.

Download nets for the Platonic solids. Download the handout for Euler's formula.

Paper construction of polyhedra. Learn the basics of constructing durable models from cardstock (65 lb. or 175 gm/m² paper).

Edge nets of cubes. Learn basic graph theory, and discover how it applies to "unfolding" a cube. In how many distinct ways can this be done? Note: For this workshop, each participant (or pair of participants) must have a cube made of a magnetic toy such as Geomag.

Slide-togethers. Build polyhedra by "sliding together" regular polygons with slits cut in them. See George Hart's website for more information.

Note: To navigate the slide show, use the arrow keys, or press "N" for next or "P" for previous. Chris, Elizabeth, Jasmine, and Mark built slide-togethers on 18 July 2008.

Origami and polyhedra. Build modular origami polyhedra models; that is, fold several identical pieces and interlock them (without glue!) to build polyhedra. 8 x 11" or A4 paper is fine for this, but teachers experienced with origami may wish to use origami paper.

Stellations of polyhedra. Learn about stellating the Platonic solids, then build some stellations! Click here to see several examples of stellations of polyhedra.

Note: Internet access is required for this workshop.

Introduction to spherical geometry. Learn about spherical geometry, an easily visualizable example of a non-Euclidean geometry. Link to algebra by computing areas of spherical triangles.

Note: A Lénárt sphere (as shown here) is required for this workshop.

Flexagons. Build flexagons out of squares (below) or triangles (as in this video.)

Introduction to spherical trigonometry. Apply plane trigonometric ideas to spherical geometry. Learn how to build geodesic domes.

Note: Participants must have a working knowledge of trigonometry. Workshop 7 is a prerequisite.

The geometry of four dimensions. Many think that the fourth dimension is time. Discover the fourth spatial dimension, and learn how to represent it in two and three dimensions.

Click here to see an interesting site on art and the fourth dimension.

last modified july 2008