I am a teacher in a high school in Georgia. I am taking a class on technology. One of the requirements is to visit a site and ask an expert a question so here goes...
The other day a colleague and I were talking about polyhedra. Is regular a term applied to polyhedra or just polygons? If so, then what would define a regular polyhedron? Would it mean all faces are regular or would it mean that all faces are identical and regular? That is, could a pyramid with equilateral triangles for lateral faces and a square base be considered regular or must the base also be an equilateral triangle?
A polyhedron is said to be REGULAR only when ALL of its parts are regular. That means that all faces must be congruent regular polygons (all equilateral triangles, or all squares, or all regular pentagons), and there must be the same number at each vertex. There are only 5 of them, all of which are described in the ELEMENTS of EUCLID (300 BC): the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The pyramid with a square base and triangular sides is an example of a polyhedron with regular faces that is not a regular polyhedron.Chris