Solid of Archimedes

In Geometry, a solid of Archimedes is a convex Polyèdre semi-regular, strongly symmetrical composed of two kinds (or more) of regular polygons meeting with identical Sommet S. They are distinct from the solid of Plato, which are composed of only one kind of polygons meeting at identical tops, and solid of Johnson, whose regular polygonal faces do not meet at identical tops. The symmetry of the solids of Archimedes excludes the members from the Groupe diédral, the prisms and the Antiprisme S.

The solid of Archimedes can all be built via the constructions of Wythoff starting from the solid of Plato with symmetries tetrahedral, octahedral and icosahedral. See polyhedral convex uniform.

Origin of the name

The solids of Archimedes draw their names from the Greek Mathématicien Archimedes, which studied them in a work currently lost. During the Rebirth, the Artist S and the Mathématicien S evaluated the pure forms and have redécouvert all these forms. This research was supplemented in the neighborhoods of 1619 by Johannes Kepler, which defines the prisms, the Antiprisme S and the known not-convex solids regular under the name of solid of Kepler-Poinsot.

Classification

There exist 13 solids of Archimedes (15 if one counts the chiral image (in a mirror) of two solids énantiomorphes, (see below). Here, the configuration of top refers to the type of regular polygons which one meets at an unspecified given top. For example, a configuration of top of (4,6,8) means that square, hexagon and octagone meet at a top (with the order taken clockwise around the top).

The number of tops is 720° divided by the angle of deflection of the top.

The cuboctaèdre and the icosidodécaèdre have uniform edges and were called quasi-regular.

The softened cube and the softened dodecahedron are chiral , they are of two forms, (lévomorphe and dextromorphe). When an object have several forms which are images mirror from/to each other in three dimensions, these forms are called énantiomorphes . (This nomenclature is also used for the chemical forms of compounds, to see enantiomer).

The duaux of the solids of Archimedes are called the solid of Catalan. With the Bipyramide S and the trapezohedrons, they are the solids with uniform faces with regular tops.

See too

  • Polyhedral semi-regular
  • polyhedral uniform
  • List of the uniform polyhedrons

References

  • Robert Williams: The Geometrical Foundation off Natural Structure: With Book Source off Design , 1979 ISBN 0-486-23729-X

External bonds

  • MathWorld
  • Owners of solids of free Archimedes
  • Owners of solids of Archimedes
  • uniform polyhedrons
  • polyhedrons actually virtual the encyclopedia of the polyhedrons
  • modular Origami
  • Polyhedral interactive 3D in Java
  • Surfaces of solids of contemporary Archimedes Designed by Tom To bore

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