The geometry behind the IQ light™ system

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[1] Platonic Solids

REGULAR POLYGONS

The regular polyhedra - solid figures with identical regular polygonal faces - were already known in classical Greece and were named after Plato, who used them in his theory of the structure of the world.

TETRAHEDRON

The equilateral triangle is the simplest regular polygon. The simplest polyhedron, the tetrahedron, can be constructed with 4 of these as its faces. A tetrahedron can be inscribed in a sphere.

The octahedron's 8 faces are also equilateral triangles. As the number of faces in a regular polyhedron increases, the form of the polyhedron becomes more spherical, a sphere having the smallest possible surface area in relation to its volume.

OCTAHEDRON

ICOSAHEDRON

The spherical form is clearly visible in the icosahedron, which is comprised of 20 equilateral triangular faces. When balanced on a point, the icosahedron can be understood as a "ring" of 10 triangular faces with a rosette of 5 faces above and another rosette of 5 below.

Besides these 3 polyhedra with triangular faces, we are familiar with one with 6 square faces, namely the regular hexahedron, also called the cube. The cube is probably the most common polyhedron, as the box shape has become a part of our culture.

HEXAHEDRON

DODECAHEDRON

The last of the 5 Platonic Solids is the regular dodecahedron, which is comprised of 12 regular pentagonal faces with three corners meeting at each apex. It may be understood as a top and a bottom face, with 2 rings of 5 faces each between the top and bottom.

When 3 regular hexagons are placed together they form a flat surface, therefore a "sphere" cannot be formed out of regular hexagonal faces only. Regular polygons with more than 6 sides cannot form a polyhedron, as 3 corners cannot meet when the corner angle is more than 120°.

Next page: [2] The Archimedean Solids

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