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.

Explanations

L1 human

A Platonic solid is a perfectly regular dice shape. All faces are the same regular polygon, and every corner looks the same. A cube is one: six equal squares, with three squares at each corner.