Stage:4 and 5
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The fact that the total angle deficiency of a polyhedron is 720 degrees, together with Euler's formula, gives the key to finding how many regular polyhedra there are (Platonic Solids) and how many semi-regular polyhedra there are (Archimedean solids) and discovering their properties (the shapes and number of faces etc.).
Mathematical reasoning & proof. Inequality/inequalities. Polyhedra. Visualising. Manipulating algebraic expressions/formulae. Topology. Networks/Graph Theory. Euler's formula. Number theory. Dynamical systems.
Published December 2000.
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