Triacontahedral rhombic

In Geometry, the rhombic triacontahedral is a convex Polyèdre with 30 faces in form of Losange S. It is the dual one of a Solide of Archimedes or Solide of Catalan. It is dual Icosidodécaèdre and a Zonoèdre.

The report/ratio of the large diagonal on the small diagonal of each face is exactly equal to the Golden section, φ, i.e. the acute angle on each faces measure 2 tan^{− 1} (1/φ) = tan^{− 1} (2), or roughly 63,43°. A rhombus thus obtained is called a rhombus of gold .

Being the dual one of a Solide of Archimedes, the triacontahedral rhombic one is uniform faces, which means that the Groupe of symmetry of the solid transitively acts on the whole of the faces . In elementary terms, this means that for two unspecified faces has and B, it exists a Rotation or a reflection of the solid which lets it occupy the same area of space during the displacement of the face has towards the face B. the triacontahedral rhombic one is also somewhat special while being one of the nine convex polyhedrons of uniform edges, the others being the five solid of Plato, the Cuboctaèdre, the Icosidodécaèdre and the rhombic Dodécaèdre.

Uses of triacontahedral rhombic

The originator Danish Holger Strøm used the triacontahedral rhombic one as a base for the design of his constructible lamp IQ-light™. (IQ for " Interlocking Quadrilaterals" (quadrilaterals interbloquants))

In some roleplays and for the use in elementary school, the triacontahedral rhombic one is used like die with thirty faces " d30 ".

See too

the rhombic Triacontahedral truncated

References

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

External bonds

the triacontahedral rhombic one on the site MathWorld
polyhedrons actually virtual – The encyclopedia of the polyhedrons
IQ-light™– The lamp of the Danish originator Holger Strøm
Ridges yours

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