![]() ![]() ![]() These join along 30 edges to form 20 vertices. Octahedron Dodecahedronįrom the Greek, meaning twelve-faced, the dodecahedron has 12 faces formed from pentagons. The shape has four pairs of parallel faces. Cube Octahedronįrom the Greek, eight-faced or eight-sided, the octahedron is eight equilateral triangles joined along 12 edges to make six vertices or corners. Cubes have three pairs of parallel faces. It is ubiquitous in our modern society and known to humans for thousands of years. Tetrahedron Cubeįrom the Greek, meaning a six-sided die, the cube is six squares joined along 12 edges to form eight vertices. Among the Platonic solids, only the tetrahedron has no faces parallel to one another. ![]() Icosahedron has 12 vertices with five triangular faces meetingįrom the Greek, meaning four-sided or four-faced, this shape is four equilateral triangles joined along six edges to form four vertices or corners. Octahedron has six vertices with four triangular faces meetingĭodecahedron has 20 vertices with three pentagonal faces meeting Tetrahedron has four vertices with three triangular faces meetingĬube has eight vertices with three square faces meeting Also, notice that the number of faces of all the Platonic solids is even.Īnother exciting feature of Platonic solids: their faces meet so that either three, four, or five faces join at vertices to form corners: Three of the five solids depend on the simplicity of the equilateral triangle. No other shapes can be created by repeating only a two-dimensional regular polygon. Here are the five Platonic Solids and their relationships to two-dimensional shapes: He had organized the known universe the solids were then always known as Platonic solids in his honor. He assigned four shapes to elements (fire, earth, water, air) and the dodecahedron to the heavens. Because the five solids each present the same face no matter how they are rotated, Plato used them in his dialogue Timaeus around 350 BCE. Greek philosopher Plato used the already existing concept of five perfect solids to connect the flawed, real world to the ideal world of his imagination. To be a Platonic solid, the tested shape must: Platonic solids Properties of Platonic solids No matter which way you look at a Platonic solid, the same-shape face stares back. Platonic solids, however, are a finite set of only five, three-dimensional shapes. Some sets in geometry are infinite, like the set of all points in a line. ![]()
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