Platonic Solids - Regular Polyhedra

At the last meeting of the Mighty Math Club, everyone enjoyed creating models of the five Platonic Solids using gumdrops, mini marshmallows, and nearly one thousand toothpicks. Some kiddos decided to build other objects, including a gorgeous replica of the Sears Tower and a biplane, but most had tremendous success with all but the dodecahedron. (That's the most wobbly of the five given the lack of triangles in the construction. This brings up some other topics for discussion along the lines of stability in building with triangles, having braces on bookshelves, etc.)

Convex regular polyhedra (poly-many; hedra-faces) are composed of faces, edges, and angles that are all congruent. These regular polyhedra are called Platonic solids. There are only five Platonic Solids - tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The name of each figure is derived from the number of its faces: respectively 4, 6, 8, 12 and 20.

Building models helps children to see the component parts and to understand the concepts of dimensionality and regularity.

The toothpicks are the edges. Just count the number used.
Each gumdrop or marshmallow is a vertex. Count them to find the number of vertices.
Paper models show the faces more clearly. Use the link below to find nets (two-dimensional paper outlines).

Euler's Rule:

If V is the number of vertices, F the number of faces, and E the number of edges of a convex regular polyhedron then the following equation is valid: V + F = E + 2

This link show how to put the models together.
http://www.youtube.com/watch?v=5QgIJOy7T7Y

Here's a link to make the Platonic Solids out of paper.
http://www.otrnet.com.au/IntegratedMathsModules/H04/H04_Platonic_Solid_Nets.pdf

This link leans in the mystical direction:
http://themathlab.com/wonders/godsdice/dicepatn.htm

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Welcome to Mathknotter where I will post my math ideas along with other trivia from my adventures as a homeschooling math tutor.