polyhedron
Sign in to saveIn geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary surface. The terms solid polyhedron and polyhedral surface are commonly used to distinguish the two concepts. Also, the term polyhedron is often used to refer implicitly to the whole structure formed by a solid polyhedron, its polyhedral surface, its faces, its edges, and its vertices.
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A polyhedron is a three-dimensional shape made up of flat polygonal faces connected by straight edges and sharp corners (called vertices). Polyhedra are fundamental objects in geometry that help us understand and describe the structure of three-dimensional space and solid forms.
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Key facts
- .title
- Examples of polyhedra
- .label1
- Definition
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- A three-dimensional example of the more general polytope in any number of dimensions.
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- Characteristics
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- number of faces, topological classification and Euler characteristic,duality,vertex figures,surface area and volume,lines as in geodesics and diagonals,Dehn invariant,symmetry group.
via Wikipedia infobox
Article
43 sectionsContents
- Definition
- General characteristics
- Number of faces
- Topological classification
- Duality
- Vertex figures
- Surface area and lines inside polyhedra
- Volume
- Dehn invariant
- Net
- Symmetries
- By elements of polyhedron
- By point group in three dimensions
- Convex polyhedra
- Other families of polyhedra
- Space-filling polyhedra
- Flexible polyhedra
- Ideal polyhedron
- Lattice polyhedron
- Polyhedral compound
- Zonohedron
- Orthogonal polyhedron
- Generalisations
- Apeirohedra
- Complex polyhedra
- Curved polyhedra
- Higher-dimensional polyhedra
- History
- Before the Greeks
- Ancient Greece
- Ancient China
- Medieval Islam
- Renaissance
- 17th–19th centuries
- 20th–21st centuries
- See also
- Notes
- References
- External links
- General theory
- Lists and databases of polyhedra
- Free software
- Resources for making physical models
In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary surface. The terms solid polyhedron and polyhedral surface are commonly used to distinguish the two concepts. Also, the term polyhedron is often used to refer implicitly to the whole structure formed by a solid polyhedron, its polyhedral surface, its faces, its edges, and its vertices.
There are many definitions of polyhedra, not all of which are equivalent. Under any definition, polyhedra are typically understood to generalize two-dimensional polygons and to be the three-dimensional specialization of polytopes (a more general concept in any number of dimensions). Polyhedra have several general characteristics that include the number of faces, topological classification by Euler characteristic, duality, vertex figures, surface area, volume, interior lines, Dehn invariant, and symmetry. A symmetry of a polyhedron means that the polyhedron's appearance is unchanged by a transformation, such as rotating and reflecting.