PLATONIC SOLIDS Audrey Johnson Characteristics of Platonic Solids

PLATONIC SOLIDS Audrey Johnson

Characteristics of Platonic Solids z. They are regular polyhedra z. A polyhedron is a three dimensional figure composed of polygons z. There are exactly five platonic solids z. All the faces are the same regular polygon z. The same number of polygons meet at each vertex

To Be a Platonic Solid… z. At least three faces must meet zthe sum of the interior angles of the sides meeting at each vertex must be less than 360 degrees y. For example, the tetrahedron is made up of equilateral triangles which consists of three 60 degree angles y 3 equilateral triangles meet at each vertex so the sum of the interior angles is 180 degrees which is less than 360 degrees

More Examples: z. Octahedron ymade up of four equilateral triangles y 4*60=240 < 360 degrees z. Icosahedron ymade up of five equilateral triangles y 5*60=300 < 360 degrees z As a result there cannot be 6 equilateral triangles since 6*60=360. If this was so the triangles would form a single-planed figure and not a solid

z. The cube: y. Made up of three squares y 3*90=270 < 360 z. As a result, if four squares met at a vertex then the interior angles would equal 360 and would form a plane and not a solid

Unique Numbers z. Tetrahedron z. Cube z. Octahedron z. Dodecahedron z. Icosahedron 4 faces 6 edges 4 vertices 6 faces 12 edges 8 vertices 8 faces 12 edges 6 vertices 12 faces 30 edges 20 vertices 20 faces 30 edges 12 vertices

Unique Relationship z. Duality y. The cube and octahedron are duals y. The icosahedron and dodecahedron are duals y. The tetrahedron is a dual to itself z. This means that one can be created by connecting the midpoints of the faces of the other

In Real Life z. The five platonic solids are ideal models of crystal patterns that occur throughout the world of minerals in numerous variations z. To the Greeks, these solids symbolized fire, earth, air, spirit, and water