polyhedra
Definition
- Noun (plural of ):
- Solid figures with flat polygonal faces: "polyhedra" are three-dimensional geometric shapes composed of multiple polygons (flat surfaces) that meet at edges and vertices. A polyhedron is the singular form, while "polyhedra" is the standard plural.
- Common examples: Cubes, pyramids, and prisms are all types of polyhedra.
Usage Examples
- Plural noun:
- The mathematician studied various polyhedra, including cubes and dodecahedra. (She examined multiple solid shapes with flat faces.)
- In geometry class, we learned that polyhedra can have different numbers of faces, such as tetrahedra (four faces) and octahedra (eight faces). (Polyhedra are classified by their face count.)
Advanced Usage
"Regular polyhedra": Polyhedra where all faces are congruent regular polygons and all vertices are identical. There are only five such shapes, known as the Platonic solids (e.g., cube, tetrahedron).
- The ancient Greeks were fascinated by regular polyhedra, believing they represented the elements. (The five Platonic solids were considered perfect forms.)
"Convex vs. concave polyhedra": Convex polyhedra have all interior angles less than 180°, while concave polyhedra have at least one "indentation."
- A cube is a convex polyhedron, but a star-shaped polyhedron is concave. (The shape's surface curves inward in some places.)
Variants and Related Words
Polyhedron (n, singular): one such solid figure.
- A cube is a polyhedron with six square faces. (A single three-dimensional shape with flat polygons.)
Polyhedral (adj): relating to or having the form of a polyhedron.
- The crystal had a polyhedral structure with many facets. (The crystal's shape was composed of multiple flat surfaces.)
Synonyms
- Multifaceted solid: a solid figure with many faces.
- Many-faced shape: a descriptive term for polyhedra.
Related Idioms
- (No common idioms exist for "polyhedra," as it is a technical term.)
Phrasal Verbs
- (No phrasal verbs are associated with "polyhedra," as it is a noun.)