dihedral

dihedral

A student measures the dihedral angle between two planes in geometry class.

Definition

  1. Adjective:

    • Having two plane faces: In geometry, "dihedral" describes an angle formed by two intersecting planes.
    • Relating to a dihedral angle: Used in contexts where two surfaces meet at a line.

  2. Noun:

    • A dihedral angle: The angle between two intersecting planes, measured in the plane perpendicular to their line of intersection.
    • Aircraft wings: In aviation, the upward or downward angle of an aircraft's wings relative to the horizontal axis, used for stability.
Usage Examples

  • Adjective:

    • The dihedral angle of a cube's faces is 90 degrees. (The angle between two adjacent faces of a cube is a right angle.)
    • The aircraft's dihedral configuration improves lateral stability. (The wings are angled upward from the horizontal.)

  • Noun:

    • In geometry class, we calculated the dihedral of a tetrahedron. (We measured the angle between two faces of a tetrahedron.)
    • The plane's dihedral was set at 5 degrees for better handling. (The wing angle was adjusted for stability.)
Advanced Usage

  • "Dihedral symmetry": A type of symmetry in geometry where an object has reflectional and rotational symmetry, often associated with regular polygons.

    • A square has dihedral symmetry of order 8. (It has 8 symmetry operations, including rotations and reflections.)

  • "Dihedral group": In mathematics, a group that describes the symmetries of a regular polygon, including rotations and reflections.

    • The dihedral group D4 is used to study the symmetries of a square. (This group includes 4 rotations and 4 reflections.)
Variants and Related Words
  • Dihedral angle (n): The angle between two intersecting planes.
    • The dihedral angle of a pyramid's faces is measured at the base edge. (The angle between the pyramid's side faces.)
  • Dihedral plane (n): A plane that bisects the dihedral angle.
    • The dihedral plane divides the angle equally between the two faces. (A plane that splits the angle.)
Synonyms
  • Two-faced: Having two faces or surfaces (less precise, used in geometry contexts).
  • Bilateral: Relating to two sides, though not specifically for angles.
Related Idioms
  • (This is a technical term with no idiomatic usage.)
Phrasal Verbs
  • (The word is primarily a noun or adjective in technical contexts.)