Lesson 1: Three-Dimensional Figures

Property

Polyhedra are split into two main families based on how they are built:

• Prism: A 3D figure with 2 parallel, congruent polygons as bases. The lateral faces connecting the bases are flat rectangles or parallelograms.
• Pyramid: A 3D figure with exactly 1 polygon base. All other flat faces are triangles that connect to a single point at the top called the apex.

Examples

• A rectangular prism (like a shoebox) has 2 rectangular bases and 4 rectangular lateral faces.
• A triangular prism, like a tent, has 2 triangular faces as bases and 3 rectangular faces as sides.
• A square pyramid has one square base and four triangular faces that meet at the top apex.

Explanation

Prisms are like shapes that have been 'stretched' straight up; whatever shape is on the bottom floor matches the top ceiling exactly. Pyramids only have a bottom floor, and their walls lean inward to meet at a single sharp point at the very top.

Property

For any polyhedron:

• A face is a flat polygonal surface
• An edge is a line segment where two faces meet
• A vertex is a point where three or more edges meet
• Euler's formula: $F + V - E = 2$ (where $F$ = faces, $V$ = vertices, $E$ = edges)

Examples