
02305901
j
1995b.00943
Persson, U.
The Platonic solids and their metric data. (De platonska kropparna och deras metrik.)
Normat 42, No. 4, 145163 (1994).
1994
Nationellt Centrum f\"or Matematikutbildning (NCM), G\"oteborgs Universitet, G\"oteborg
SV
G30
inscribed circles
circumscribed circles
The objective of the article is to compute the metric data of the computation of volume and area, as well as the computations of the inscribed and the circumscribed radii. The computations are trivial for the simpler Platonic solids but require some effort for the case of the icosahedron and the dodecahedron. Our first approach is an elementary, headon attack, using no clever ideas. Our second approach is to follow Coxeter and introduce the hybrid solids. Then one is able, in a very succinct, elegant and uniform way, to get simple trigonometric expressions for all the data for all the solids. Along the way we take time to explain the combinatorial data (number of vertices, edges and faces) of the Platonic solids, and relate them to spherical trigonometry. (orig.)