Do the Platonic solids occur in nature?
PLATONIC SOLIDS IN NATURE. These regular structures are commonly found in nature, but they are generally hidden from our perception. The first manifestation of Platonic solids in nature is in the shape of viruses. Of all Platonic solids only the tetrahedron, cube, and octahedron occur naturally in crystal structures.
Where do Platonic solids occur in nature?
Occurrence of Platonic Solids in Nature The tetrahedron, hexahedron and octahedron all occur in crystals, but there are a total of 45 other forms of crystals. Neither the icosahedron nor the dodecahedron occurs in crystals (Smith, 1982, pg 12).
Do Platonic solids Tessellate?
By the way, a polyhedron is called a tessellation polyhedron if at least one of its e-nets tiles the plane. In fact, there are exactly 23 tessellation polyhedra found among all regular faced poly- hedra (four Platonic solids, 18 JZ solids and one regular hexagonal antiprism) [1].
What do the Platonic solids represent?
The 5 platonic solids are considered cosmic solids due to their connection to nature that was discovered by Plato. The cube represents the earth, the octahedron represents the air, the tetrahedron represents the fire, the icosahedron represents the water, and the dodecahedron represents the universe.
Which is the best definition of a Platonic solid?
A Platonic solid is a regular, convex polyhedron in a three-dimensional space with equivalent faces composed of congruent convex regular polygonal faces. The five solids that meet this criterion are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Some sets in geometry are infinite, like the set of all points in a line.
How are Platonic solids used in magical work?
The platonic solids can also be used to represent the elements in magical working, and also have the metaphysical properties of the elements that they are associated with. They could be brought into the practice in order to invoke these energies into your working much like sigils of the elements.
What did Euclid write about the Platonic solids?
Euclid completely mathematically described the Platonic solids in the Elements, the last book (Book XIII) of which is devoted to their properties. Propositions 13–17 in Book XIII describe the construction of the tetrahedron, octahedron, cube, icosahedron, and dodecahedron in that order.
How many Platonic solids can a topological proof be made?
Pentagonal faces: Each vertex is 108°; again, only one arrangement of three faces at a vertex is possible, the dodecahedron. Altogether this makes 5 possible Platonic solids. A purely topological proof can be made using only combinatorial information about the solids.