Platonic solid

Definition

A Platonic solid is a convex polyhedron $P$ in $\mathbb{R}^3$ with these two properties:

the faces of $P$ are regular polygons that are all congruent to each other;
the same number of faces meet at each vertex of $P$ .

Remarks

If each face has $p$ sides and $q$ faces meet at each vertex, the solid has the Schläfli symbol $\{p, q\}$ . The five Platonic solids are the regular tetrahedron $\{3, 3\}$ , the cube $\{4, 3\}$ , the regular octahedron $\{3, 4\}$ , the regular dodecahedron $\{5, 3\}$ and the regular icosahedron $\{3, 5\}$ . See the classification. They have the name of Plato, who wrote about them in the dialogue Timaeus.

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Polyhedron concept
Regular polygon concept
Platonic solid definition

Tag	`00BETAJNZ4`
URI	`m2://00BETAJNZ4`
Kind	definition
Writing	W1 stated
MSC	51M20
Defines	Platonic solid
Uses	Polyhedron, Regular polygon

Platonic solid

Definition

Remarks

Reading path

Further reading

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