Gourt > Science > Math > Geometry > Polytopes (3)
In geometry polytope means, first, the generalization to any dimension of polygon in two dimensions, and polyhedron in three dimensions. Beyond that, the term is used for a variety of related mathematical concepts. This is analogous to the way the term square may be used to refer to a square-shaped region of the plane, or just to its boundary, or even to a mere list of its vertices and edges along with some information about the way they are connected. The term was coined by Alicia Boole, the daughter of logician George Boole.
The Platonic solids, or regular polytopes in three dimensions, were a major focus of study of ancient Greek mathematicians (most notably Euclid's Elements), probably because of their intrinsic aesthetic qualities. In modern times, polytopes and related concepts have found important applications in computer graphics, optimization, search engines and numerous other fields.
Convex polytopes
More on [ Polytope ]
Sculpture and Art :: Geometry
Tessellations :: Recreations
Can't even read Polytopes or nothin' #boooooo
artemisthethird (Chelsea Robertson) Sun, 03 Jan 2010 01:38:00 -0000
Can't even read Polytopes or nothin' #boooooo
Polygons, Polyhedra, Polytopes - Regular, rectified, and truncated polytopes with normal and hidden-detail-removed projections. Images, animations, and links.
Meta Description: [ Polygons, polyhedra, and polytopes. ]
Polytopes - Enumeration, cartesian coordinates of vertices, naming, and counting the shapes.
Meta Description: [ Naming, counting and measuring polyhedra or polytopes. ]
Guy's Polyhedra Pages - Vertex figures, filling, faceting diagrams, stellation, defining polytopes through generators, trimethoric and trisynaptic polyhedra, space-filling polyhedra, lost stellations of the icosahedron, and links.
Pick's Theorem - Describes a theorem for finding an area of simple lattice polygons. Includes proof and Java applet simulation.
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Polyhedra, Platonic Solids, Polytopes - Definitions, pictures, templates, and coordinates of the regular 3d and 4d polytopes. Also includes waterman polyhedra, polar and star spheres, and the time star.
Regular Polytopes - Derivation of volume equations for regular polygons, polyhedra, and polytopes, with images.
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Sliceform Models by John Sharp - Three-dimensional objects constructed by slotting together a series of planar cross sections made from card. Downloadable templates in PDF, PS and Word formats.
The Charged Particles Model - Polytopes and optimal packing of p points in n dimensional spheres. Contains a java applet based on a model which allows for generation of multidimensional regular and semi-regular polytopes.
Meta Description: [ Polytopes and optimal packing of p points in n dimensional spheres. ]
The Geometry Junkyard - Comprehensive list of links to sites on geometric properties of the shapes.
The Mathematical Atlas - Polytopes and Polyhedra - Collection of discussions regarding volume, vertices, dissection, g-holed tori, and other subjects.
Zome Edu - Educational toys used to teach geometry and model building to create squares, spheres, stars and other regular shapes with sticks and connecting pieces. Products include kits and lesson plans.
Meta Description: [ Zome a creative, fun, and versatile educational toy, a teaching tool. Used by scientists, engineers, and architects. With Zome, math is child's play ]
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