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Acute Golden Rhombohedron


GoldenRhombohedra

A golden rhombohedron is a trigonal trapezohedron (and therefore rhombohedron with congruent rhombic faces) whose faces consist of six equal golden rhombi. There are two distinct golden rhombohedra: an acute one and an obtuse one.

The acute golden rhombohedron is a zonohedron and one of the five golden isozonohedra. It is implemented in the Wolfram Language as PolyhedronData["AcuteGoldenRhombohedron"].

AcuteGoldenRhombohedronNet

A net of the acute golden rhombohedron is illustrated above.

The acute golden rhombohedra with edge length a has tip-to-tip height

 h=sqrt(3+6sqrt(sqrt(5)))a,
(1)

surface area,

 S=(12)/5sqrt(5)a^2,
(2)

and volume

 V=1/5sqrt(10+2sqrt(5))a^3.
(3)

Twenty acute golden rhombohedra can be combined to form a solid rhombic hexecontahedron (Kabai 2002, p. 171).


See also

Golden Isozonohedron, Golden Rhombohedron, Obtuse Golden Rhombohedron, Rhombohedron, Trigonal Trapezohedron

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References

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.

Cite this as:

Weisstein, Eric W. "Acute Golden Rhombohedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AcuteGoldenRhombohedron.html

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