Dissecting a Cube into a Golden Acute Rhombohedron and Three Congruent Rectangular Solids

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This Demonstration shows a seven-piece dissection of a cube into an acute golden rhombohedron and three congruent rectangular solids. The viewpoint changes with the slider. Any one of the rectangular solids can be reassembled into a quarter of a Bilinski dodecahedron.

References

[I] I. Hafner and T. Zitko, "From Dissection of the Cube to Space Filling with Prolate Rhombohedra and Rhombic Dodecahedra of the Second Kind," Visual Mathematics 4(2), 2002. www.mi.sanu.ac.rs/vismath/hafner4/SFVisual.html.

External Links

Dissecting a Cube into a Rhombohedron and Three Congruent Cubes
Dissecting a Cube into an Obtuse Rhombohedron, Three Congruent Rectangular Solids and Two Congruent Cubes
Golden Rhombohedron (Wolfram MathWorld)
Acute Golden Rhombohedron (Wolfram MathWorld)
Dissection of a Cube to a Quarter of a Rhombic Dodecahedron of the Second Kind
Dissecting a Rhombic Triacontahedron into Twenty Congruent Cubes
26-Piece Dissection of a Cube
Golden Isozonohedron (Wolfram MathWorld)
Rhombic Icosahedron (Wolfram MathWorld)
Kepler's Rhombic Triacontahedron and Rhombic Icosahedron
Approximate Rhombic Icosahedron
Double Rhombic Icosahedron
Golden Rhombic Solids with Nets

Permanent Citation

Izidor Hafner
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​"Dissecting a Cube into a Golden Acute Rhombohedron and Three Congruent Rectangular Solids"​
​http://demonstrations.wolfram.com/DissectingACubeIntoAGoldenAcuteRhombohedronAndThreeCongruent/​
​Wolfram Demonstrations Project​
​Published: April 1, 2019