Kepler's Rhombic Solids

​
cube
rhombic dodecahedron
triacontahedron
convex hull
0
show net
Kepler discovered his rhombic solids as the convex hulls of compounds of a Platonic solid and its dual. The rhombic dodecahedron derives from the cube-octahedron compound; the triacontahedron derives from the dodecahedron-icosahedron compound; and the cube from the stella octangula. The nets of the compounds are also shown.

References

[1] P. R. Cromwell, Polyhedra, Cambridge: Cambridge University Press, 1997 pp. 152–153.

External Links

Dodecahedron-Icosahedron Compound (Wolfram MathWorld)
Rhombic Triacontahedron (Wolfram MathWorld)
Inverting the Rhombic Dodecahedron
Symmetric Decompositions of a Rhombic Triacontahedron
Decomposition of a Double Triacontahedron
Stella Octangula (Wolfram MathWorld)
Stella Octangula
Rhombic Dodecahedron Made of Four Rhombohedra
Decomposing a Rhombic Dodecahedron into a Trapezoid-Rhombic Dodecahedron
Honeycomb

Permanent Citation

Izidor Hafner
​
​"Kepler's Rhombic Solids"​
​http://demonstrations.wolfram.com/KeplersRhombicSolids/​
​Wolfram Demonstrations Project​
​Published: July 1, 2014