Q:
# Why Are There Only 5 Platonic Solids?

As defined by Plato, the essential properties of a Platonic solid are: all sides are convex regular polygons of equal size, all of the faces intersect at their edges and nowhere else, and the same number of faces meet at each of the solid's vertices. Only five polygons fit all of these criteria: the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron.

Continue ReadingEuclid wrote a geometric proof for the criteria of Platonic solids in his work, "Elements." The proof includes four rules as follows: each vertex must be in contact with at least three sides; the sum of the angles at each vertex must be less than 360 degrees; the angles at all vertices must be equal; and the common face can only be a triangles, square, or pentagon, as faces with six or more sides have angles that are too great to be valid.

Platonic solids are lauded for their symmetry and beauty, and Plato himself described the solids as being symbolic of the fundamental forces of the world. He matched the tetrahedron with the sharpness of fire, the cube with the rigidity of earth, the octahedron with the lightness of air, the dodecahedron with "what god used to craft the heavens" (later labelled "aether" by Aristotle), and the icosahedron with the flowing nature of water.

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Q:
## What Are the Properties of a Cuboid?

A: A cuboid has its own surface area and volume, and it is a three-dimensional solid plane figure containing six rectangular faces, eight vertices and twelve ... Full Answer >Filed Under: -
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## How Many Faces, Edges and Vertices Does a Sphere Have?

A: A sphere has no faces, edges or vertices. By definition, it is a curved three-dimensional geometric figure whose surface is defined as the set of all the p... Full Answer >Filed Under: -
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## How Many Edges Does a Hexagonal Pyramid Have?

A: A pyramid with a hexagon-shaped base has 12 edges, seven faces and seven vertices (points where edges meet). The qualities of a polyhedron are intrinsicall... Full Answer >Filed Under: -
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## How Many Vertices Does a Hexagonal Prism Have?

A: A hexagonal prism has 12 vertices, along with eight faces and 18 edges. This shape has two hexagonal sides, as well as size rectangular sides that connect ... Full Answer >Filed Under: