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EnchantedLearning.com Regular Polyhedra or Platonic Solids: Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron |
 TETRAHEDRON Make a paper tetrahedron, a pyramid formed by four triangles. |
 TETRAHEDRON FROM A SMALL ENVELOPE This is an incredibly easy way to make a tetrahedron (a pyramid) from a small envelope. |
 CUBE Make a paper cube, a solid geometric figure with six square faces. |
 OCTAHEDRON Make a paper octahedron. An octahedron is an eight-sided regular geometric solid. |
 DODECAHEDRON Make a paper dodecahedron. A dodecahedron is a twelve-sided regular geometric solid composed of pentagons. |
 ICOSAHEDRON Make a paper icosahedron. An icosahedron is a twenty-sided regular geometric solid composed of equilateral triangles. |
The five regular polyhedra were discovered by the ancient Greeks. The Pythagoreans knew of the tetrahedron, the cube, and the dodecahedron; the mathematician Theaetetus added the octahedron and the icosahedron. These shapes are also called the Platonic solids, after the ancient Greek philosopher Plato; Plato, who greatly respected Theaetetus' work, speculated that these five solids were the shapes of the fundamental components of the physical universe.
| Platonic Solid | Number of Faces | Shape of Faces | Number of Faces at Each Vertex | Number of Vertices | Number of Edges | Dual (The Platonic Solid that can be inscribed inside it by connecting the mid-points of the faces) |
|---|---|---|---|---|---|---|
| Tetrahedron | 4 | Equilateral Triangle (3-sided) | 3 | 4 | 6 | Tetrahedron |
| Cube | 6 | Square (4-sided) | 3 | 8 | 12 | Octahedron |
| Octahedron | 8 | Equilateral Triangle (3-sided) | 4 | 6 | 12 | Cube |
| Dodecahedron | 12 | Pentagon (5-sided) | 3 | 20 | 30 | Icosahedron |
| Icosahedron | 20 | Equilateral Triangle (3-sided) | 5 | 12 | 30 | Dodecahedron |
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