dihedon

A student measures the angle of a dihedon formed by two intersecting planes.

Definition

1. Noun:
   • Geometry: A "dihedron" is a polyhedron with two faces, typically a degenerate polyhedron formed by two polygons sharing the same set of edges. In mathematics, it is often used to describe a type of spherical tiling or a limiting case of a prism.

Usage Examples

• (A shape with only two faces.)
• (A geometric figure with two faces.)

Advanced Usage

• "dihedral angle": The angle between two intersecting planes, often measured in a dihedron.

  • The dihedral angle of a regular dihedron is constant. (The angle between its two faces.)

• "spherical dihedron": A tiling of a sphere by two congruent lunes (curved polygons).

  • A spherical dihedron is formed by dividing the sphere into two equal parts. (A spherical shape with two faces.)

Variants and Related Words

• Dihedral (adj): relating to or having two faces or planes.

  • The dihedral symmetry of the crystal is evident. (Symmetry with two planes.)

• Dihedrally (adv): in a manner involving two faces or planes.

  • The structure is arranged dihedrally. (Arranged with two faces.)

Synonyms

• Two-faced polyhedron: a polyhedron with exactly two faces.
• Bifacial polyhedron: a polyhedron having two distinct faces.

Phrasal Verbs

(None applicable — "dihedron" is a noun and does not commonly form phrasal verbs.)

Related Idioms

(None applicable — "dihedron" is a technical term without common idiomatic usage.)