The Use of Platonic Solids in Probability Concepts

Abstract

The author discusses the geometries of Platonic solids and their relevance to some probabilistic situations. Specifically, what is highlighted is the fact that Platonic solids such as tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron, are all solids each of them bounded by a definite number of congruent faces. Just like what is usually done in hexahedron, each of the solid's faces will be numbered and the probability of getting a specific number for a certain experiment- an outcome generating activitiy is determined. Ordinarily, two cubes or a pair of dice are used in measuring the probability of getting a certain sum if they are rolled in a game of chance. As an extended treatment, one may use two tetrahedrons, or two octahedrons, to come up with 4x4-matrix or 8x8-matrix tables respectively, to enumerate all the possible elements of the sample space for the situation. This is not difficult to imagine if one is familiar with the 6x6 table formed to list all the possibilities of numbers showing up if a pair of dice is thrown. The odd pairing of, say a hexahedron and a tetrahedron can also be explored. Needless to say, the use of two dodecahedrons or two icosahedrons can be very stimulating to the students. To top it all, any pair-combination of these Platonic solids can without a doubt deepen and enhance the concepts of probability.