How Many Platonic Solids Are There?


Quick Answer

There are five platonic solids. A platonic solid is a 3-D shape where each face is the same regular polygon, and the same number of polygons meet at each corner, or vertex, according to Math is Fun.

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Full Answer

The five platonic solids are the cube, tetrahedron, octahedron, dodecahedron and icosahedron, according to Math Is Fun. In a cube, three identical squares meet at each corner and each cube face is an identical square. A tetrahedron is made up of three triangle faces that meet at each corner. An octahedron has four triangles in each corner and eight triangular faces. Dodecahedrons contain three pentagons at each corner and have 12 pentagonal faces. Finally, icosahedrons have five triangles at each corner and 20 triangular faces.

Remember that when the internal angles of the corners are added together, the sum must be less than 360 degrees. If a shape has 360 degrees or more at a vertex, it is not a platonic solid because the shape would be flat. According to Math is Fun, an easy equation to remember is Euler's Formula, which indicates that the number of faces, plus the number of corner points, minus the number of edges always equals two. If the equation doesn't equal two, then the shape is not a platonic solid.

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