Polygons and PolyhedraPlatonic
At the beginning of this course we defined A regular polygon is a polygon in which all sides have the same length and all interior angles have the same size.
In a regular polyhedron all The faces of a polyhedron are the polygons which make up its surface. The “corners” of a polyhedron are called its vertices. A Platonic solid is a polyhedron where every face is a regular polygon with the same number of edges, and where the same number of faces meet at every vertex. There are only five different Platonic solids: the Tetrahedron, Cube, Octahedron, Dodecahedron and Icosahedron. Plato (c. 425 – 347 BCE) was a philosopher in ancient Greece, and – together with his teacher Socrates and his student Aristotle – laid the very foundation of Western philosophy and science. Plato founded the Academy of Athens, the first higher learning institution in the Western world. His many writings on philosophy and theology, science and mathematics, politics and justice, make him one of the most influential thinkers of all time.
So what do the Platonic solids look like – and how many of them are there? To make a three-dimensional shape, we need at least