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Polyhedron

In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') 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…

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Characteristics
number of faces, topological classification and Euler characteristic, duality, vertex figures, surface area and volume, lines as in geodesics and diagonals, Dehn invariant, symm…
Definition
A three-dimensional example of the more general polytope in any number of dimensions.

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Overview

Definition

General characteristics

Symmetries

Convex polyhedra

Other families of polyhedra

Generalisations

Higher-dimensional polyhedra

History

General theory

Free software

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Map overview Semantic statistics

Polyhedron

Nodes354
Edges353
Triples212
Avg. degree1.99
Density0.00565
Components1

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Polyhedron

Top relations

related to Free software · 22
Polyhedron → Aachen Computer Graphics Group, An, Conway Polyhedron Notation, Developed, Explorer, Features, Free, Hyperspace Star Polytope Slicer, Java, Models, OBJ, OpenVolumeMesh, Plethora, PNG, Polyhedra, Polyhedronisme Archived, RWTH Aachen University, The, User Manual, VRML2
related to Dehn invariant · 14
Polyhedron → Another, Bolyai, Dehn, Euclidean, Every, Gerwien, Hilbert's, In, It, Max Dehn, Sydler, The, The Dehn, To
related to By elements of polyhedron · 11
Polyhedron → All, For, If, Individually, Kepler, Nevertheless, Platonic, Poinsot, The, There, When
related to General theory · 11
Polyhedron → Crystals, CS1, Dr, Eric, MathWorld, Polyhedra, Polyhedra PagesUniform Solution, Uniform Polyhedra, Wayback MachineSymmetry, Weisstein, Zvi Har'El Archived
related to Lattice polyhedron · 10
Polyhedron → An, Convex, Dehn, Reeve, Sommerville, Stanley, The, The Ehrhart, There, This
related to Space-filling polyhedra · 10
Polyhedron → Dehn, Delone, Every, Federov, Hill, Parallelohedra, Some, Such, These, Voronoi
related to Curved polyhedra · 9
Polyhedron → Curved, However, If, Many, Platonic, Some, Two, Weaire-Phelan, When
related to Lists and databases of polyhedra · 9
Polyhedron → Contains, Electronic Geometry Models, Paper Models, Polyhedra, Polyhedron Models, The Encyclopedia, Uniform, Virtual, Virtual Reality Polyhedra
related to Number of faces · 9
Polyhedron → Classical Greek, English, For, Greek, Numeral, Platonic, Polyhedra, Table, The
is a · 8
Polyhedron → convex hull of a finite set of ideal points, convex hull of its vertices, convex polyhedron defined in three-dimensional hyperbolic space, convex polyhedron with hexagonal and pentagonal faces, planar graph with three-connected, polyhedron whose Euler characteristic is less than or equal to 0, solid or surface that can be described by its vertices, sum of the areas of its faces

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Important terminology

polyhedra faces convex vertices edges regular symmetry many surface two may vertex also polyhedral volume solids space polygons group three-dimensional

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
PolyhedronCharacteristicsnumber of faces, topological classification and Euler characteristic, duality, vertex figures, surface area and volume, lines as in geodesics and diagonals, Dehn invariant, symm…1.00infobox
PolyhedronDefinitionA three-dimensional example of the more general polytope in any number of dimensions.1.00infobox
Polyhedronis aconvex hull of its vertices0.90text
Polyhedronis aconvex polyhedron defined in three-dimensional hyperbolic space0.90text
Polyhedronis asolid or surface that can be described by its vertices0.90text
Polyhedronis apolyhedron whose Euler characteristic is less than or equal to 00.90text
Polyhedronis asum of the areas of its faces0.90text
Polyhedronis aconvex polyhedron with hexagonal and pentagonal faces0.90text
Polyhedronis aplanar graph with three-connected0.90text
Polyhedronis aconvex hull of a finite set of ideal points0.90text
the skew apeirohedra have also been called polyhedrainstance ofshapes with infinitely many faces0.80text
Weaire-Phelan bubblesinstance ofTwo important types are bubbles in froths and foams0.80text

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