Look around the room. Hunt for cubes, spheres, cylinders, cones, pyramids, prisms. They're everywhere once you see them.
Spin the solid
Hexagonal prism
faces
8
8
edges
18
18
vertices
12
12
V − E + F = 12 − 18 + 8 = 2
drag to rotate
Faces, edges, vertices
For every solid you find, count three things: F (flat faces), E (edges where faces meet), V (corner points). Write them in a table — a cube is F=6, E=12, V=8.
Euler's formula links them all: V − E + F = 2 for any convex solid. Cube: 8 − 12 + 6 = 2. Square pyramid: 5 − 8 + 5 = 2. It always works.
Your turn
A triangular prism has 2 triangular ends and 3 rectangular sides. How many vertices, edges and faces? Does Euler's formula hold?
Common 3D shapes in the wild
- Cube — dice, sugar cube, building block
- Cylinder — soup can, candle, drum
- Sphere — ball, orange, bubble
- Cone — ice cream cone, traffic cone, party hat
- Pyramid — Egyptian pyramid, tent
Count faces, edges and vertices for each. Euler's formula: V − E + F = 2 (for any convex solid).