Twenty equilateral triangles — five meeting at every corner. The most 'round' of the Platonic solids, which is why it shows up as the D20 die, as virus capsids, and as the basis of geodesic domes.
Spin the solid
Icosahedron
faces
20
20
edges
30
30
vertices
12
12
V − E + F = 12 − 30 + 20 = 2
drag to rotate
Icosahedron facts
- 20 faces (equilateral triangles), 30 edges, 12 vertices — Euler: 20 − 30 + 12 = 2.
- 5 faces meet at every vertex (5 × 60° = 300° < 360°).
- It's the dual of the dodecahedron — swap faces and vertices.
- Its 12 vertices can be placed as the corners of three perpendicular golden rectangles — φ again.
Volume from the edge length
≈ 2.182 a³ — the biggest-volume Platonic solid for a given edge.
Drag the solid above to spin it: hunt for a vertex and count the five triangles fanning around it. That five-fold pinwheel at every corner is the icosahedron's signature.