polyhedron
/'pɔli'hedrən/
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Definition
- Noun:
- A solid geometric figure in three dimensions that is completely bounded by flat polygonal surfaces called faces. The faces meet at straight-line segments called edges, and the edges meet at points called vertices.
Examples of Usage
- Noun:
- A cube is a common example of a polyhedron.
- The architect designed a building with the complex shape of an irregular polyhedron.
- In geometry class, we learned to calculate the volume of a polyhedron.
Advanced Usage
- Regular Polyhedron: A polyhedron whose faces are all identical regular polygons and whose vertices are all identical. There are only five convex regular polyhedra (Platonic solids).
- The tetrahedron, cube, and dodecahedron are all regular polyhedra.
- Convex Polyhedron: A polyhedron where any line segment connecting two points on its surface lies entirely inside or on the polyhedron.
- Most basic geometric shapes, like prisms and pyramids, are convex polyhedra.
- Euler's Formula for Polyhedra: A fundamental theorem stating that for a convex polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the formula V - E + F = 2.
- We used Euler's formula to verify the structure of the model polyhedron.
Variants and Related Words
- Polyhedral (adjective): Of or relating to a polyhedron; having the shape or form of a polyhedron.
- The sculpture had a striking polyhedral form.
- Polyhedra (noun): The standard plural form of , often used in academic or technical contexts.
- The study focused on the properties of various polyhedra.
Synonyms
- Solid (in a geometric context): A three-dimensional figure.
- Geometric solid: A three-dimensional geometric shape.
Different Meanings
- The term is highly specific to geometry and three-dimensional space. It does not have common metaphorical or idiomatic meanings outside of mathematical and related technical fields (e.g., computer graphics, crystallography).
Noun
- a solid figure bounded by plane polygons or faces