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Regular 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


TETRAHEDRON

Make a paper tetrahedron, a pyramid formed by four triangles.
tetrahedron
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.
Regular Polyhedron Matching

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.
Regular Polyhedron Matching

Unfolding 3-D Shapes: Cube and Tetrahedron Nets

Draw an unfolded cube and tetrahedron. Or go to the answers.
Regular Polyhedron Matching

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.

hexaflexagon done 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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