Rhombohedron

A rhombohedron is a polyhedron bounded by six diamonds. It is a parallelepiped with edges of equal length.

Applied rhombohedron

Art and Nature

Albrecht Dürer is in his partly mathematically inspired graphics Melencolia I is a specially trimmed rhombohedron, which would be by this modification, with all its vertices on a spherical surface.

Maurits Cornelis Escher used in his impossible figures also different rhombohedron with previews and structural development.

Calcite crystal

Rhombohedral crystals of calcite by the example

Elongated and flattened rhombohedron

Crystal structure theory

The shape of the rhombohedron is found in nature as a crystal form and at the atomic level in crystal lattices again. The rhombohedron is only available in the trigonal crystal system; with the ( ortho ) rhombic crystal system it has - nothing to do - despite the similar name.

The Farbrhomboeder

A rhombohedron, in which the short diagonal of the outer surfaces is the same length as the Rhomboederseiten, provides an absolutely symmetric parallelepiped dar. Two exterior surfaces are parallel to each other over here. Each diamond-shaped outer surface is composed of two equilateral triangles. Cuts to a rhombohedron along the short diagonal of the exterior surfaces, there are three parts, two tetrahedra and an octahedron. These three bodies are in turn completely symmetrical. All outer surfaces of these three new geometric bodies are equilateral triangles.

The remarkable cuts on the rhombohedron

Axes, diagonals and edges in Kueppers' Farbrhomboeder

The Farbrhomboeder met by Harald Kueppers the geometric solution for the color theory. Every point within said body corresponding to a color stimulus. That means each of these (color) points is defined by its three vectors potentials. Through compression and distortion of the color rhombohedral convert it into RGB or CMY color space, naturally with different ratios between the color values ​​.