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Acute Golden Rhombohedron

GoldenRhombohedra

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"].

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+6/(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.

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

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