id: 02305901
dt: j
an: 1995b.00943
au: Persson, U.
ti: The Platonic solids and their metric data. (De platonska kropparna och
deras metrik.)
so: Normat 42, No. 4, 145-163 (1994).
py: 1994
pu: Nationellt Centrum för Matematikutbildning (NCM), Göteborgs Universitet,
Göteborg
la: SV
cc: G30
ut: inscribed circles; circumscribed circles
ci:
li:
ab: 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,
head-on 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.)
rv: