Dihedral Angle
Worked Example
Problem: Two walls of a room meet along a vertical edge. One wall faces due north and the other faces due east. What is the dihedral angle between the two walls?
Step 1: Identify the shared edge. The two walls meet along a vertical line (the corner of the room).
Step 2: In each wall, draw a horizontal line perpendicular to the vertical edge. One line points due north; the other points due east.
Step 3: Measure the angle between these two horizontal lines. North to east is a quarter turn.
θ=90°
Answer: The dihedral angle between the two walls is 90°.
Why It Matters
Dihedral angles appear throughout geometry and science. In chemistry, the dihedral angle between bonded atoms determines a molecule's three-dimensional shape and properties. In architecture and engineering, understanding the angle between structural planes is essential for designing roofs, folded-plate structures, and hinged mechanisms.
Common Mistakes
Mistake: Measuring the angle between the planes at a random direction rather than perpendicular to the shared edge.
Correction: The dihedral angle is defined using two rays that are each perpendicular to the line of intersection (the shared edge) and lie in their respective planes. Measuring at any other direction gives the wrong value.
Related Terms
- Angle — General concept that dihedral angle extends to 3D
- Plane — The two flat surfaces that form the angle
- Polyhedron — Solid whose faces meet at dihedral angles
- Normal to a Plane — Normals can also define the dihedral angle