Key Concepts: Three-Dimensional Figures

Polyhedra

A polyhedron (plural: polyhedra) is a solid bounded by polygons called faces. The segments where faces meet are edges, and the points where edges meet are vertices.

Common 3D Figures

• Prism: Two congruent, parallel polygonal bases connected by rectangular faces. Named by the shape of the base (triangular Prism, rectangular Prism, etc.).
• Pyramid: One polygonal base with triangular faces meeting at a single Point (apex).
• Cylinder: Two congruent, parallel circular bases connected by a curved surface.
• Cone: One circular base tapering to a Point (apex).
• Sphere: The set of all points equidistant from a center Point.

Euler's Formula

For any convex polyhedron: V − E + F = 2, where V = vertices, E = edges, F = faces.

Cross Sections

A cross section is the shape formed when a Plane intersects a solid figure.