What shape has 20 triangular faces?
Quick answer
A solid shape with exactly 20 triangular faces is called an icosahedron, from Greek eikosi (“twenty”) and hedra (“seat” or face). The regular icosahedron, made of 20 identical equilateral triangles, has 12 vertices (corners) and 30 edges.
The five Platonic solids
A Platonic solid has identical regular faces, with the same number meeting at each corner. Only five exist:
| Solid | Faces | Face shape | Vertices | Edges |
|---|---|---|---|---|
| Tetrahedron | 4 | Triangles | 4 | 6 |
| Cube | 6 | Squares | 8 | 12 |
| Octahedron | 8 | Triangles | 6 | 12 |
| Dodecahedron | 12 | Pentagons | 20 | 30 |
| Icosahedron | 20 | Triangles | 12 | 30 |
The ancient Greek philosopher Plato linked four of them to the elements: fire, earth, air and water, which he assigned to the icosahedron.
Euler’s formula
For any simple solid like these, Vertices − Edges + Faces = 2. For the icosahedron: 12 − 30 + 20 = 2. Swiss mathematician Leonhard Euler described this in the 1750s.
Where icosahedrons appear
| Example | Why |
|---|---|
| 20-sided dice (d20) | Used in games like Dungeons & Dragons |
| Viruses | Many virus shells (capsids) are icosahedral, an efficient way to build a strong shell from repeated proteins |
| Geodesic domes | Designs based on subdivided icosahedrons |
| Soccer balls | The classic ball is a “truncated icosahedron,” with 12 pentagons and 20 hexagons |
| Magic 8 Ball | The answer inside floats on a 20-sided die |
Duals
The dodecahedron and icosahedron are “duals”: if you put a dot in the center of each face of one and connect the dots, you get the other.
Other shapes to know
For a shape with one hole, see what a doughnut shape is called in math. For the theorem about right triangles, see what the Pythagorean theorem is.
Still curious?
Jump to a random question from the archive.