There can be only 5 Platonic Solids


Of all the activities we’ve done at my afterschool math club, learning about and making platonic solids is one of the kids’ favorites.

Platonic solids are convex polyhedra with the following characteristics:

  1. all its faces are the same
  2. all faces are regular polygons (all edges and angles of the faces are the same)
  3. none of its faces intersect except at their edges, and
  4. the same number of faces meet at each of its vertices.

platonicThe 5 platonic solids are:

  1. Tetrahedron – 4 triangular faces
  2. Cube (Hexahedron) – 6 square faces
  3. Octahedron – 8 triangular faces
  4. Dodecahedron – 12 pentagonal faces
  5. Icosahedron – 20 triangular faces



You can get foldable platonic solid printouts at the Interactives: Platonic Solids page at This webpage also has an interactive activity where kids can identify the number of faces, edges, and vertices for each solid and try to determine the relationship between these three properties.

Below are parts 1 and 2 of an out-of-print video about platonic solids, that is available on YouTube. The first explains the properties of platonic solids and why there only five. The second shows different views of the platonic solids, platonic solids found in nature, and the property of “duality”.

One thought on “There can be only 5 Platonic Solids

  1. Pingback: How to Make an Envelope Tetrahedron | hollymath

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