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Lectures on the Icosahedron (Dover Phoenix Editions)

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... but it's a real pity this edition doesn't include any of the figures which used to be present in the German-language editions. They were actually useful to better grasp the concepts discussed.

Also, though far less important as it frequently happens with this kind of heavily theoretical topics, there's a lack of numerical examples.

This is a famous book first published in German in 1884. In a fairly elementary way Professor Klein finds algebraic equations for the tetrahedron, cube and icosahedron by means of their rotational and reflection symmetry.Unfortunately there are no Figures such as provided by Coxeter,Regular Complex Polytopes,Cambridge Univ. Press 1991, probably because the facilities were not available.
The tetrahedron,cube and icosahedron are all Platonic solids which the ancient Greeks recognised as basic to the construction of the physical universe and their finite symmetries are the basis of considerable study in particle physics today. Interestingly enough I plotted Klein's equation for the tetrahedron (using a computer program unavailable in 1884)and found a cube which is well-known to be isomorphic to the tetrahedron.