Definition

1. Noun:
   • A geometric figure formed by three or more planes that meet at a common point (the vertex): A polyhedral angle is the spatial region enclosed by the faces (planes) that extend from a single vertex.

Usage

• The term is used in geometry to describe a specific three-dimensional shape originating from a point.
• It is typically discussed in relation to polyhedra, as the corners of polyhedra are polyhedral angles.
• Example: "The cube has polyhedral angles where three square faces meet at each vertex."

Examples

• Noun:
  • The tetrahedron is composed of four polyhedral angles.
  • Calculating the measure of a polyhedral angle requires understanding the angles between its faces.

Advanced Usage

• "Solid angle": While related, a solid angle is a measure of the amount of the field of view an object covers, whereas a polyhedral angle refers to the specific geometric figure formed by planar faces.
  • The concept of a polyhedral angle is crucial for defining the solid angle subtended by a polyhedron's vertex.

Variants and Related Words

• Polyhedron (n): A solid figure with many plane faces, typically more than six.
  • A cube is a common example of a polyhedron.
• Vertex (n): The common point where the planes of a polyhedral angle meet.
  • All planes intersect at the vertex of the angle.
• Face (n): Each of the plane surfaces that bound a polyhedron and form the sides of a polyhedral angle.
  • Each face of the polyhedral angle is a flat plane.

Synonyms

• Solid angle (in a closely related conceptual sense regarding spatial extent at a vertex).
• Corner (in a general, non-technical sense for a polyhedron).

Related Phrases

• Trihedral angle: A specific type of polyhedral angle formed by exactly three planes.
  • A corner of a rectangular room forms a trihedral angle.

Noun

1. the space enclosed by three or more planes that intersect in a vertex