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 More Math ActivitiesGo to a K-3 Shapes Page EnchantedLearning.comRegular Polyhedra or Platonic Solids:Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron

There are only five geometric solids that can be made using a regular polygon and having the same number of these polygons meet at each corner. The five Platonic solids (or regular polyhedra) are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.

History of Platonic Solids

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 Solids - Info
Platonic Solid Picture Number of Faces Shape of Faces Number of Faces at Each Vertex Number of Vertices Number of Edges Unfolded Polyhedron (Net) 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 Regular Pentagon
(5-sided)
3 20 30 Icosahedron
Icosahedron 20 Equilateral Triangle
(3-sided)
5 12 30 Dodecahedron
Note: Euler's formula states that (The Number of Faces) + (The Number of Vertices) - (The Number of Edges) = 2

Printable Worksheets and Activities
 TETRAHEDRONMake a paper tetrahedron, a pyramid formed by four triangles. TETRAHEDRON FROM A SMALL ENVELOPEThis is an incredibly easy way to make a tetrahedron (a pyramid) from a small envelope. CUBEMake a paper cube, a solid geometric figure with six square faces. OCTAHEDRONMake a paper octahedron. An octahedron is an eight-sided regular geometric solid. DODECAHEDRONMake a paper dodecahedron. A dodecahedron is a twelve-sided regular geometric solid composed of pentagons. ICOSAHEDRONMake a paper icosahedron. An icosahedron is a twenty-sided regular geometric solid composed of equilateral triangles. Match Each Regular Polyhedron to Its Name and Its Unfolded FormDraw lines between each Platonic solid (regular polyhedron), its name, and its unfolded form. Polyhedra: tetrahedron, cube, octahedron, dodecahedron, icosahedron. Or go to the answers. Unfolding 3-D Shapes: Cube and Tetrahedron Nets Draw an unfolded cube and tetrahedron. Or go to the answers. Polyhedra: Fill-in-the-Blanks Fill in the name, number of faces, net, number of vertices, number of edges, and shape of the faces for five polyhedra (tetrahedron, cube, octahedron, dodecahedron, and icosahedron). Or go to the answers.

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