A golden rhombohedron is a rhombohedron whose faces consist of congruent golden rhombi. Golden rhombohedra
are therefore special cases of a trigonal trapezohedron
as well as zonohedra.
There are two distinct golden rhombohedra: the acute golden rhombohedron and obtuse golden
rhombohedron. Both are built from six golden rhombi
and comprise two of the five golden isozonohedra.
These polyhedra are implemented in the Wolfram
Language as PolyhedronData["AcuteGoldenRhombohedron"]
and PolyhedronData["ObtuseGoldenRhombohedron"],
respectively.
The acute and obtuse golden rhombohedra with edge length 
both have surface area
 |
(1)
|
and have volumes
respectively.
The two shapes are the tiles of the Ammann-Kramer-Neri tiling, a three-dimensional analogue of Penrose
tiles (Dietl and Eschenburg 2017).
See also
Acute Golden Rhombohedron,
Ammann-Kramer-Neri Tiling,
Golden
Isozonohedron,
Golden Ratio,
Golden
Rhombus,
Obtuse Golden Rhombohedron,
Rhombic Hexecontahedron,
Rhombohedron,
Trigonal Trapezohedron,
Zonohedron
Explore with Wolfram|Alpha
References
Dietl, R. M. K. and Eschenburg, J.-H. "The Icosahedral Quasiperiodic Tiling and Its Self-Similarity." J. Geom. 108,
319-354, 2017. https://doi.org/10.1007/s00022-016-0342-2.Kabai,
S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica.
Püspökladány, Hungary: Uniconstant, pp. 169 and 171, 2002.Livio,
M. The
Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New
York: Broadway Books, p. 206, 2002.Referenced on Wolfram|Alpha
Golden Rhombohedron
Cite this as:
Weisstein, Eric W. "Golden Rhombohedron."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GoldenRhombohedron.html
Subject classifications
