polyhedron

Definitions

• WordNet 3.6
• n polyhedron a solid figure bounded by plane polygons or faces
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Webster's Revised Unabridged Dictionary
• Polyhedron (Geom) A body or solid contained by many sides or planes.
• Polyhedron (Opt) A polyscope, or multiplying glass.
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Century Dictionary and Cyclopedia
• n polyhedron In geometry, a solid bounded by plane faces.
• n polyhedron In optics, a multiplying glass or lens consisting of several plane surfaces disposed in a convex form, through each of which an object is seen; a polyscope.
• n polyhedron In bot.,in Hydrodictyon or water-net, one of the special angular cells with horn-like processes formed by the swarm-cells produced in the zygospore, within each of which a new cœnobium is developed.
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Chambers's Twentieth Century Dictionary
• n Polyhedron pol-i-hē′dron a solid body with many bases or sides
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Etymology

Webster's Revised Unabridged Dictionary
NL., fr. Gr. with many seats or sides; poly`s many + a seat or side: cf. F. polyèdre,
Chambers's Twentieth Century Dictionary
Gr. polys, many, hedra, a base.

Usage

In literature:

An edifice is no longer an edifice; it is a polyhedron.
"Notre-Dame de Paris" by Victor Hugo
In turn it was a sphere, a disk, a pyramid, a pentahedron, a polyhedron.
""Where Angels Fear to Tread" and Other Stories of the Sea" by Morgan Robertson
Book VII relates to polyhedrons, cylinders, and cones.
"The Teaching of Geometry" by David Eugene Smith
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In news:

Indeed, many beaded beads can be viewed as polyhedra, where the hole through the middle of each bead corresponds to a polyhedron's edge.
Polyhedrons consist of triangles, squares, pentagons, hexagons, and other polygons that are joined together to form closed, three-dimensional objects.
Different rules for linking various polygons generate different types of polyhedrons.
The faces of a polyhedron can have different sizes and shapes, just as long as each one is a polygon.
The polyhedron itself can have a hole (or two or more).
Consider what happens when a vertex of one tetrahedron pierces the face of a second tetrahedron to form a new, more complicated polyhedron.
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In science:

The set of bistochastic matrices of size N can be viewed as a convex polyhedron in RN 2 .
Random unistochastic matrices
The volume of the polyhedron of bistochastic matrices was computed by Chan and Robbins .
Random unistochastic matrices
The boundary of ΣB 3 is obtained from spectra of the members of the convex polyhedron of the bistochastic matrices of size 3.
Random unistochastic matrices
At the same time, for every ﬁnite-dimensional subspace of c0 its unit bal l is a polyhedron.
Classification of Banach Spaces --its Topological and Cardinality Properties
The conditions Min(Ps , L) ≤ x ≤ Max(Ps , L) deﬁne a parallelepiped K (possible not maximal dimension) in V and the bsemiample divisors Li generate a convex rational polyhedron R ⊂ V containing the diagonal [Ps , L] of K.
On Zariski decomposition problem
In fact, for each face X of the polyhedron ∂UΦ , there exists at least one Pi such that the preceding statement is true for Pi whenever u ∈ X .
Random Surfaces
By Lemma 4.3.3, UΦ is the interior of a convex polyhedron and by Lemma 4.3.7, σ is a bounded, continuous function on the closure of UΦ .
Random Surfaces
The symmetry group of the octahedron is identical to the symmetry group of the cube since the octahedron is the dual polyhedron of the cube.
Quantum circuits for single-qubit measurements corresponding to platonic solids
The icosahedron is the dual polyhedron of the dodecahedron.
Quantum circuits for single-qubit measurements corresponding to platonic solids
In this section, we let X be an m-dimensional compact polyhedron with metric.
Conley Index Theory and Novikov-Morse Theory
Proposition 4.7 Let X be a compact polyhedron.
Conley Index Theory and Novikov-Morse Theory
Theorem 5.1 Let X be a compact polyhedron with a metric d.
Conley Index Theory and Novikov-Morse Theory
Here χ(X ) is the Euler characteristic number of the compact polyhedron.
Conley Index Theory and Novikov-Morse Theory
Theorem 5.6 (Vanishing theorem) Let X be a compact polyhedron with a metric d.
Conley Index Theory and Novikov-Morse Theory
Measure µβ and polyhedron Pβ , of course, do not depend on the choice of Λ; thus, no index Λ in notation µβ and Pβ .
Grade of Membership Analysis: One Possible Approach to Foundations
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