trihedron

A student draws a trihedron on the chalkboard.

Definition

1. Noun:
   • A geometric figure formed by three planes meeting at a point: In mathematics, a "trihedron" is a solid angle or a three-sided pyramid-like shape created by three intersecting planes that share a common vertex.

Usage Examples

• Noun:
  • In geometry class, we studied the properties of a trihedron formed by three planes. (A three-sided angle at a point.)
  • The crystal structure can be modeled as a trihedron with sharp edges. (A geometric figure with three faces.)

Advanced Usage

• "Trihedral angle": a synonym often used interchangeably with "trihedron" to describe the angle at the vertex where three planes meet.

  • The trihedral angle of the pyramid was measured to be 90 degrees. (The angle formed by three planes.)

• "Trihedron in polyhedra": In the study of polyhedra, a trihedron occurs at vertices where exactly three faces meet, such as in a cube's corner.

  • Each corner of a cube is a trihedron because three faces intersect there. (A vertex with three faces.)

Variants and Related Words

• Trihedral (adj): having three faces or sides.

  • The trihedral prism has a triangular cross-section. (The prism has three faces.)

• Trihedron's (possessive form): belonging to or associated with a trihedron.

  • The trihedron's edges are all of equal length. (The edges of the trihedron.)

Synonyms

• Three-plane angle: an angle formed by three planes.
• Trihedral angle: a solid angle with three faces.

Related Idioms

• There are no common idioms involving "trihedron," as it is a highly technical mathematical term.

Phrasal Verbs

• There are no phrasal verbs associated with "trihedron," as it is a noun used in formal contexts.