# Earth Grids

12 13 Each of the the five Platonic Solids opposite is made up of faces of just one regular polygon, with all vertices lying on a sphere. Their perfect symmetry makes them an integral part of planetary grid research. The tetrahedron has four vertices and four triangular faces, the octahedron six vertices and eight triangular faces, the cube eight vertices and six square faces, the icosahedron twelve vertices and twenty triangular faces, while the dodecahedron has twenty vertices and twelve pentagonal faces. The earliest written evidence of them goes back to the era of Pythagoras and Plato 427347 BC. Plato writes in the Phaedo 110b The real Earth, viewed from above, resembles a ball made of twelve pieces of leather, variegated and marked out in different colors.... This appears to reference a dodecahedron. It is certainly the first mention of the Earth grid. In the Timaeus, he also says the Demiurge used a twelvesided form as a pattern for the World. However, hundreds of neolithic carved stones, discovered in Northern Scotland and Europe see below, perfectly resemble the Platonic solids and date to 2000 years before Plato. Geometer Keith Critchlow believes that they could have been used to map the stars, function as navigational aids or act as props to teach students spherical geometry. The plaTonic solids timeless polyhedra in ancient days Octahedron Icosahedron Dodecahedron Tetrahedron Cube Above The Tetrahedral and CubeOctahedral system, common in crystals and widely used in architecture. The three Platonic solids which embody this system are shown. This system contains numerous root 2 and 3 proportions. Above The IcosiDodecahedral system, common in viruses, pollens, plankton and other living things. Two Platonic solids embody this system, which is rich is golden section proportions. Far Left The CubeOctahedral grid. Left The Tetrahedron. Below Left The Octahedron. Below The Cube. Left The IcosiDodecahedral grid. Above left The Icosahedron. Above right The Dodecahedron. The Icosahedron and the Dodecahedron are each others duals, which is to say that each is constructed from the centres of the others faces.