Twelve regular pentagons stitched together — three meeting at each corner. One of the five Platonic solids, and the shape of a D12 die. The Greeks thought it represented the cosmos itself.
Spin the solid
Dodecahedron
faces
12
12
edges
42
42
vertices
20
20
V − E + F = 20 − 42 + 12 = -10
drag to rotate
Dodecahedron facts
- 12 faces (regular pentagons), 30 edges, 20 vertices — Euler: 12 − 30 + 20 = 2.
- 3 faces meet at every vertex — three pentagons (3 × 108° = 324° < 360°, so it folds up).
- It's the dual of the icosahedron — 12 faces ↔ 12 vertices, 20 vertices ↔ 20 faces.
- Pentagons are full of the golden ratio φ ≈ 1.618, so φ runs all through the dodecahedron's measurements too.
Drag to spin it. Each face is a regular pentagon; three meet at every corner, and the spinning wireframe makes the dual-with-the-icosahedron symmetry easy to see.
Your turn
Each face of a dodecahedron is a regular pentagon. What is the size of one of its interior angles?