Polyhedra - Sides? Faces?
Date: 10/13/97 at 19:13:19 From: Maria Carrow Subject: Polyhedra How many sides does a tetrahedron have? How many sides does an icosahedron have?
Date: 10/14/97 at 16:23:04 From: Doctor Chita Subject: Re: Polyhedra Dear Maria: The objects you've asked about are solids, not plane figures. The ending "-hedron" tells you that these are three-dimensional shapes that have "faces" rather than "sides" like a triangle or a square. A regular "polyhedron" is a solid having faces (surfaces) in the shape of a regular polygon. The other parts of a polyhedron are called edges, where the faces meet, and vertices, corners where vertices of the faces coincide. [What would hurt if you sat on one. :-) ] The prefix of each word tells you something about the solid. In the case of a tetrahedron, the prefix "tetra-" means four. Therefore, there are four triangular faces in a tetrahedron. An icosahedron has 20 triangular faces. The prefix "icosa-" is from the Greek word "eikosi" meaning 20. These two regular polyhedra (plural of "polyhedron") are special because they are two of the five Platonic solids, the simplest of which is the tetrahedron. The others are the cube (with 6 square faces, as you know), the octahedron (with 8 triangular faces), and the dodecahedron (with 12 faces that are regular pentagons). There is also an interesting relationship among the number of faces (f), edges (e), and vertices (v) of a polyhedron. The mathematician Leonard Euler discovered that in every polyhedron, not just the Platonic solids, f - e + v = 2. For example, in a cube, f = 6, e = 12, and v = 8, and 6 - 12 + 8 = 2. Try this relation on other polyhedra - for example, the Great Pyramid in Egypt. (Remember, it has a rectangular base.) I'll bet you didn't think the answer to your question would be so interesting, did you? Hope this helps. -Doctor Chita, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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