Deltoidal icositetrahedron
The Deltoidalikositetraeder (also called Deltoidikositetraeder ) is a convex polyhedron composed of 24 deltoids and is among the the Catalan bodies. It is dual to the Rhombicuboctahedron and has 26 vertices and 48 edges.
In crystallography and mineralogy the Deltoidalikositetraeder is often ( shortened ) called Ikositetraeder, also works as a trapezohedron or Leucitoeder ( it is the typical crystal form of Leucits ).
Formation
- Will the 14 boundary faces of a cuboctahedron square and triangular pyramids with the edge length and fitted, creates a general Deltoidalikositetraeder if and are. The cuboctahedron has inscribed it the edge length ( d i a diagonal of the kite s, u ).
- By connecting the midpoints of four edges that collide in each corner of the room Rhombenkuboktaeders, creates a trapezium whose inscribed circle radius of the deltoids, the boundary surface of the Deltoidalikositetraeders, is at the same time. In this particular type all face angle ( ≈ 138 ° 7 ' 5 ") are equal, and there is a uniform sphere radius edges.
- Furthermore, the Deltoidalikositetraeder can be regarded as a triple cut " bloated " cube, which with its 24 square boundary surfaces topologically equivalent.
Related polyhedra
Inscribed cube
Inscribed octahedron
Inscribed cuboctahedron
Formulas
For the polyhedron
For the deltoid
Occurrence
In nature, for example, leucite, analcime and Spessartin crystallize preferably in the form of Deltoidalikositetraedern. Even with other minerals of the garnet group or the fluorite come Deltoidalikositetraeder ago as crystal form. The Deltoidalikositetraeder, which is the form { hll } ( with h> l), is either a special form of crystal class m3m, a limiting form of the Pentagonikositetraeders in the crystal class 432 or a limiting form of the Disdodekaeders in the crystal class m3.
Analcime
Spessartin