Dissection of Half an Obtuse Golden Rhombohedron and Half an Acute Golden Rhombohedron into a Cube

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This Demonstration shows a dissection of a half of an obtuse golden rhombohedron and a half of an acute golden rhombohedron into a cube.

For a volume of the obtuse golden rhombohedron of

2ϕ

, the volume of the acute golden rhombohedron equals

, where

is the golden ratio. Thus this Demonstration implies the identity

ϕ+

. Note that

can be replaced by

in this identity:

ϕ×

References

[1] W. W. R. Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover Publications, 1987 p. 161.

[2] I. Hafner and M. Budin, "Dissection of Cubes and Golden Rhombic Solids," in Aproged's 5th International Conference, Geometrias '19: Polyhedra and Beyond, Porto, Portugal (V. Viana, ed.), Porto: Aproged, 2019 pp. 91–93. www.aproged.pt/geometrias19proceedings.html.

External Links

A Golden Ratio Dissection

Dissection of a Cube to a Quarter of a Rhombic Dodecahedron of the Second Kind

Dissecting and Reassembling a Cube into Three Different Solids

Golden Rhombohedron (Wolfram MathWorld)

Golden Isozonohedron (Wolfram MathWorld)

A Dissection of a Prolate Golden Rhombohedron

Dissection of the Oblate Golden Rhombohedron

Dissecting an Acute Golden Rhombohedron into a Rectangular Solid

Dissection of a Rhombohedron into a Right Prism with the Same Base

Dissecting Two Cubes into Golden Rhombohedra

Dissecting a Rhombohedron into Two Congruent Rhombohedra

Permanent Citation

Izidor Hafner, Mateja Budin

"Dissection of Half an Obtuse Golden Rhombohedron and Half an Acute Golden Rhombohedron into a Cube"
http://demonstrations.wolfram.com/DissectionOfHalfAnObtuseGoldenRhombohedronAndHalfAnAcuteGold/
Wolfram Demonstrations Project
Published: September 26, 2019