Polyhedron sentence example

polyhedron
  • More briefly, the figure may be defined as a polyhedron with two parallel faces containing all the vertices.
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  • The points thus obtained are evidently the vertices of a polyhedron with plane faces.
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  • Probably the best way to make a sphere is to make a polyhedron with a large number of sides.
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  • Each stage of refinement defines a new, denser, polyhedron whose vertices are related to local sets of vertices of the original.
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  • In the first place, each of these figures may be conceived as an orthogonal projection of a closed plane-faced polyhedron.
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  • Clerk Maxwell, who showed amongst other things that a reciprocal can always be drawn to any figure which is the orthogonal projection of a plane-faced polyhedron.
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  • Normally by the end of the calculation less than one half of the entries in BOX actually are used to define the limiting polyhedron.
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  • In origami this term is often misused to mean any star-like form produced by adding pyramids to the faces of a convex polyhedron.
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  • The head of this list is iteratively decimated and the list updated until a target number of vertices for the sparse polyhedron is met.
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  • This is one of the Platonic solids, and is treated in the article Polyhedron, as is also the derived Archimedean solid named the "truncated tetrahedron"; in addition, the regular tetrahedron has important crystallographic relations, being the hemihedral form of the regular octahedron and consequently a form of the cubic system.
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  • The "regular icosahedron" is one of the Platonic solids; the "great icosahedron" is a Kepler-Poinsot solid; and the "truncated icosahedron" is an Archimedean solid (see Polyhedron).
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  • The "ordinary dodecahedron" is one of the Platonic solids (see Polyhedron).
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  • The "small stellated dodecahedron," the "great dodecahedron" and the "great stellated dodecahedron" are Kepler-Poinsot solids; and the "truncated" and "snub dodecahedra" are Archimedean solids (see Polyhedron).
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  • One needs to select all atoms in the cage - these will be the vertices of the final polyhedron.
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  • The mensuration of the cube, and its relations to other geometrical solids are treated in the article Polyhedron; in the same article are treated the Archimedean solids, the truncated and snubcube; reference should be made to the article Crystallography for its significance as a crystal form.
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  • If the figure be entirely to one side of any face the polyhedron is said to be " convex, " and it is obvious that the faces enwrap the centre once; if, on the other hand, the figure is to both sides of every face it is said to be concave, " and the centre is multiply enwrapped by the faces.
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  • A polyhedron is said to be the hemihedral form of another polyhedron when its faces correspond to the alternate faces of the latter or holohedral form; consequently a hemihedral form has half the number of faces of the holohedral form.
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  • The correspondence of the faces of polyhedra is also of importance, as may be seen from the manner in which one polyhedron may be derived from another.
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  • If we take any polyhedron with plane faces, the null-planes of its vertices with respect to a given wrench will form another polyhedron, and the edges of the latter will be conjugate (in the above sense) to those of the former.
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  • Octahedra having triangular faces other than equilateral occur as crystal forms. See Polyhedron and Crystallography.
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