How many platonic solids are there

It also has 6 edges and 6 vertices. At each vertex three edges meet. The cube has 6 faces. Each is a square. It also has 12 edges and 8 vertices. The octahedron has 8 faces.

A platonic solid is a 3D shape where each face is the same as a regular polygon and has the same number of faces meeting at each vertex. A regular, convex polyhedron with identical faces made up of congruent convex regular polygons is called a platonic solid.

There are 5 different kinds of solids that are named by the number of faces that each solid has. These 5 solids are considered to be associated with the five elements of nature i. Earth, air, fire, water, and the universe. Plato, who was studying the platonic solids closely, associated each shape with nature.

The 5 times of platonic solids are:. Plato associated the tetrahedron with fire, the cube with earth, the icosahedron with water, the octahedron with air, and the dodecahedron with the universe.

Platonic solids have their own unique properties that distinguish them from the rest. They are mentioned below:. There are 5 types of platonic solids with unique properties and different shapes.

Let us learn more about the 5 types:. A tetrahedron is known as a triangular pyramid in geometry. The tetrahedron consists of 4 triangular faces, 6 straight edges, and 4 vertex corners. It is a platonic solid which has a three-dimensional shape with all faces as triangles. The properties of a tetrahedron are:. Sloane, N. Waterhouse, W. Exact Sci.

Webb, R. Wells, D. Middlesex, England: Penguin Books, pp. London: Penguin, pp. Wenninger, M. Cambridge, England: Cambridge University Press, pp. Polyhedron Models.

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Wolfram Language » Knowledge-based programming for everyone. When we add up the internal angles that meet at a vertex, it must be less than degrees. And, since a Platonic Solid's faces are all identical regular polygons , we get:. In a nutshell: it is impossible to have more than 5 platonic solids, because any other possibility violates simple rules about the number of edges, corners and faces we can have together. It says: for any convex polyhedron which includes the Platonic Solids the Number of Faces plus the Number of Vertices corner points minus the Number of Edges always equals 2.

To see why this works, imagine taking the cube and adding an edge say from corner to corner of one face. We get an extra edge, plus an extra face:. Next, think about a typical platonic solid. What kind of faces does it have, and how many meet at a corner vertex?