Solid of Catalan

In Mathematical, a solid of dual Catalan or archimédien , is a dual Polyèdre of a Solide of Archimedes. The solids of Catalan were named thus in the honor of the Belgian Mathématicien Eugene Catalan which was the first to describe them in 1865.

The solids all of Catalan are convex S. They are uniform faces but not of uniform tops, because of the fact that the duaux archimédiens is uniform tops and not of uniform faces. It should be noted that with the difference of the solid of Plato and the solid of Archimedes, the faces of the solids of Catalan are not not regular polygons. On the other hand, the figures of tops of the solids of Catalan are regular, and have diédraux angles. Moreover, two of the solids of Catalan have uniform edges: the rhombic Dodecahedron and the rhombic Triacontahedral . Those are the duaux ones of the two solids of quasi-regular Archimedes.

Like their duaux partners archimédiens, there exist two chiral solids of Catalan : the pentagonal Icositétraèdre and the pentagonal Hexacontaèdre. Each one of them has two forms énantiomorphes. Without counting these versions énantiomorphes, there exist 13 solids of Catalan on the whole.

References

Catalan Eugene Memory on the Theory of the Polyhedrons. J. the Polytechnic school (Paris) 41,1-71, 1865.
Alan Holden Shapes, Space, and Symmetry . New York: Dover, 1991.
Magnus Wenninger Dual Models Cambridge, England: Cambridge University Near, 1983.
Robert Williams The Geometrical Foundation off Natural Structure: With Book Source off Design . Dover Publications, Inc, 1979, ISBN 0-486-23729-X

External bonds

Solid of Catalan – Site MathWorld
Duaux archimédiens – Polyhedrons actually virtual
Solid of interactive Catalan in Java

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