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	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

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.
Match Each Regular Polyhedron to Its Name and Its Unfolded Form Draw 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.

	For instructions how to make a 3-D hexaflexagon (a figure made from six tetrahedrons), click here.
	For instructions how to make a hexagonal prism (not a Platonic solid, but an interesting geometric solid), click here.

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