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General Information 19
Nine regular solids
Various types of polyhedra have exercised the minds of mathematicians
throughout the ages, including Euclid, whose great
work The Elements was intended not so much as a geometry
text book but as an introduction to the five regular solids
known to the ancient world. This work starts with the
equilateral triangle and ends with the construction of the
icosahedron.
The five so-called Platonic solids form the first and simplest
group of polyhedra. They have regular faces, all of which
touch one another, and the lines which make up any of the
vertices form a regular polygon.
Further variations of the regular polyhedra, unknown in
ancient times, are the Kepler-Poinsot star polyhedra. In all
four cases the vertex figures spring from pentagrams. These
polyhedra can be formed from the regular dodecahedron and
icosahedron.
Kepler (1571–1630) found the two stellated dodecahedra,
and Poinsot (1777–1859) discovered the great dodecahedra
and the great icosahedron.
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