Together with icosahedron (20 faces) they are known as the Platonic Solids.
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A trapezoid is not a platonic solid. There are only five platonic solids. They are the tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron.
A die can have any number of sides; one-sided dice are a joke in the form of a sphere and two-sided dice are often a simple coin shape. Others use platonic solids to give the required number of sides.The most commonly used are six-sided dice, noted as d6 and usually cubic, but other common numbers include d4 (a tetrahedron), d8 (an octahedron), d10 and d12 (a dodecahedron).
The thirteenth book in Euclids Elements has no specific title, but covers the Pythagorean proofs of Theaetetus (c. 417-369 bc) and the construction of the five regular Platonic solids (pyramid, cube, octahedron, dodecahedron, icosahedron) inside a given sphere.
You could classify a regular tetrahedron, which is a platonic sold, as a cone.
Many solids have no rectangular faces, including such forms as the hexagonal pyramid and the regular octahedron.