3D Shapes Explorer

Geometry · Axiom Academy

Exploring solid figures in three dimensions — and the language we use to measure them. While 2D shapes like squares and circles are flat, 3D shapes (also called solids ) have depth — they take up space in the real world. Every solid is built from three kinds of parts: faces , edges , and vertices . You don't have to take that on faith — watch them appear on a cube, one kind at a time. Watch the cube turn, then watch its parts light up in order: first the 6 flat faces , then the 12 edges where faces meet, then the 8 corner vertices . Each count climbs as the parts highlight. Faces are the flat surfaces, edges are where two faces meet, and vertices are the corner points. (A cube: 6 + 8 − 12 = 2 — Euler's formula holds.) Every solid raises two natural questions: how much fits inside it, and how much surface wraps around it. Watch the same 3×3×3 cube answer both — first it fills with little unit cubes (that's volume ), then its faces peel off and unfold flat (that's surface area ). Two different measurements, two different units. The amount of space inside a 3D shape — the unit cubes that fill it. Think: how much water could it hold? The total area of all outer surfaces — the faces, unfolded flat. Think: how much wrapping paper would it take? Volume counts cubes inside (cubic units); surface area counts squares on the outside (square units).

This is the written version of the interactive lesson above. See the full Geometry course.