An acute golden rhombohedron is the acute member of the two golden rhombohedra. Both are trigonal trapezohedra
(and therefore rhombohedra with congruent
rhombic faces) whose faces consist
of six equal golden rhombi.
The acute golden rhombohedron is a zonohedron and one of the five golden isozonohedra. It is
implemented in the Wolfram Language
as PolyhedronData["AcuteGoldenRhombohedron"].
A net of the acute golden rhombohedron is illustrated above.
The acute golden rhombohedra with edge length 
has tip-to-tip height
 |
(1)
|
surface area,
 |
(2)
|
and volume
 |
(3)
|
Twenty acute golden rhombohedra can be combined to form a solid rhombic
hexecontahedron (Kabai 2002, p. 171).
Together with the obtuse golden rhombohedron, this is a tile of the Ammann-Kramer-Neri
tiling, a three-dimensional analog of Penrose tiles
(Dietl and Eschenburg 2017).
See also
Ammann-Kramer-Neri Tiling,
Golden Isozonohedron,
Golden
Rhombohedron,
Obtuse 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
Acute Golden Rhombohedron
Cite this as:
Weisstein, Eric W. "Acute Golden Rhombohedron."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AcuteGoldenRhombohedron.html
Subject classifications
