Small rhombicosidodécaèdre

The small rhombicosidodécaèdre is a Solide of Archimedes. It has 20 triangular faces regular, 30 square faces regular, 12 pentagonal faces regular, 60 tops and 120 edges.

The name rhombicosidodécaèdre refers to the fact that the 30 square faces are placed in the same plans as the 30 faces of the rhombic Triacontaèdre which is dual Icosidodécaèdre.

It can also be called a wide dodecahedron or an icosahedron extended starting from the operations of truncation of the Solide uniform.

__TOC

Geometrical relations

If you extend a Icosaèdre by moving the faces of the origin of a certain distance, without changing the orientation or the size of the faces and that you made the same thing with his dual, the Dodécaèdre and that you fill the square holes in the result, you obtain small a rhombicosidodécaèdre. Consequently, it has the same number of triangles as an icosahedron and the same number of pentagons as a dodecahedron, with a square for each with dimensions of edge.

The kits Zome to manufacture geodetic domes and other polyhedrons use balls split like connectors. The balls are small rhombicosidodécaèdres " développés" , with the squares replaced by rectangles. The development is selected so that the resulting rectangles are gold rectangles.

Cartesian coordinates

The Cartesian coordinated for the tops of small a rhombicosidodécaèdre centered in the beginning are

$(\ pm 1, \ pm 1, \ pm \ tau^3)$ ,

(\ pm \ tau^3, \ pm 1, \ pm 1)

(\ pm 1, \ pm \ tau^3, \ pm 1)

(\ pm \ tau^2, \ pm \ tau, \ pm 2 \ tau)

(\ pm 2 \ tau, \ pm \ tau^2, \ pm \ tau)

(\ pm \ tau, \ pm 2 \ tau; , \ pm \ tau^2)

(\ pm (2+ \ tau), 0, \ pm \ tau^2)

(\ pm \ tau^2, \ pm (2+ \ tau), 0)

(0, \ pm \ tau^2, \ pm (2+ \ tau))

where $\ tau = \ frac {(1+ \ sqrt {5})}{2}$ is the Golden section.

See too

the Dodecahedron
the Icosahedral
the Icosidodécaèdre
the Small rhombicuboctaèdre
the Large rhombicosidodécaèdre (icosidodécaèdre truncated)

References

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

External bonds

uniform polyhedrons
polyhedrons actually virtual the encyclopedia of the Polyhedrons

Random links: