Later students did hands-on experiments to introduce them to the 3-D Euclidean shapes, such as cutting and gluing a soccer ball and analyzing the platonic solids
in terms of the relation between its number of edges, faces and vertices.
, the first class of such shapes, are well known.
But I found "A Geometric Analysis of the Platonic Solids
and Other Semi-Regular Polyhedra" to be very reader-friendly.
A Geometic Analysis Of The Platonic Solids
And Other Semi-Regular Polyhedra (science)
All Platonic solids
are convex regular polyhedra symmetrical about their centers.
are 3-dimensional shapes that look identical from every vertex and are composed of only one type of regular polygon (1).
The cosmos is both an abstract set of laws--the four elements, the perfect circular orbits, Platonic solids
etc--and a particular history, a one-off event, a singular evolutionary chain.
The primary thesis in the Mysterium cosmographicum is that God created the (Copernican) universe to express the five platonic solids
(the cube, tetrahedron, octahedron, icosahedron, and dodecahedron).
Students can also mark edges, vertices, and faces to highlight these aspects on Platonic solids
, Archimedian solids, other geometric solids, and the mathematical relationships related to these solids were the objects of study.
There are still people who feel uneasy when they learn that Isaac Newton spent most of his intellectual energy on alchemy and biblical prophecies, and that Johannes Kepler's three laws of planetary motion are embedded in elaborate theories concerning the Platonic Solids
and the Harmony of the Spheres.
The same technique can be applied to the other four regular geometric shapes, or Platonic solids
, that have been known since classical times.