---
tag: 00BETAJNZ4
kind: definition
name: Platonic solid
msc: [51M20]
defines: 017E5PRS1Q
uses: [0325SGSJAR, 01KJJ9A400]
sources:
  - url: https://en.wikipedia.org/wiki/Platonic_solid
    locator: lead section
  - url: https://en.wikipedia.org/wiki/Platonic_solid
    locator: Combinatorial properties
  - url: https://en.wikipedia.org/wiki/Platonic_solid
    locator: History
---

## Definition

A Platonic solid is a convex [[polyhedron|0325SGSJAR]] $P$ in $\mathbb{R}^3$ with these two properties:
- the faces of $P$ are [[regular polygons|01KJJ9A400]] 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|0M4TCS0RRG]].
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.