Platonic solids are composed of polygons—all the same shape. Some of the five Platonic solids are familiar to us: the tetrahedron, made of 4 triangles, the cube, made of 6 squares, even the intriguing icosahedron, the 20-sided dice, known best to Dungeon and Dragon players. The octahedron is 2 pyramids that connect along their square bottoms. The delightful dodecahedron is less familiar: 12 pentagons forming polyhedra. We’ll start by making models of these shapes. Next we will explore the even more intriguing and conceptually brilliant Archimedean Solids. Many are “truncated” or trimmed- off Platonic Solids. Unlike Platonic Solids, they are composed of different polygons: the truncated cube (made of triangles and octagons), the truncated octahedron (hexagons and squares), the cuboctahedron (triangles and squares), rhombicuboctahedron (also triangles and squares), the truncated icosahedron (aka the soccer ball, its modern version envisioned by Buckminster Fuller, made of hexagons and pentagons), and the icosidodecahedron (triangles and pentagons). We’ll make models of these Archimedean Solids, and you can take these geometric prizes home. Archimedes of Syracuse (287-212 BCE), considered to be the greatest Greek mathematician, discovered these geometric forms, but his writings were lost. Pappas, one of the last Greek mathematicians, referred to them in his writings, so we know they existed. They were lost from, say, 220 BCE until 1619 (about 1,800 years!) — until Johannes Kepler, the great German mathematician, rediscovered them. So in this hands-on course, we will keep rediscovering them in our time, too.
John Chamberlain is a Retired Lexington English teacher and writer with a passion for Science.