An obtuse golden rhombohedron is the obtuse member of the two golden rhombohedra. Both are trigonal trapezohedra
and rhombohedra whose faces are six congruent golden rhombi.
The obtuse golden rhombohedron is a zonohedron and one of the five golden isozonohedra. It is
implemented in the Wolfram Language
as PolyhedronData["ObtuseGoldenRhombohedron"].
A net of the obtuse golden rhombohedron is illustrated above.
The obtuse golden rhombohedra with edge length 
has tip-to-tip height
 |
(1)
|
surface area
 |
(2)
|
and volume
 |
(3)
|
Together with the acute golden rhombohedron, this is a tile 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 Rhombohedron,
Rhombohedron,
Trigonal
Trapezohedron
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
Obtuse Golden Rhombohedron
Cite this as:
Weisstein, Eric W. "Obtuse Golden Rhombohedron."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ObtuseGoldenRhombohedron.html
Subject classifications
