It is interesting to note that, “the lines along which a Rubik’s cube can be turned are, projected onto a sphere, similar, topologically identical, to a rhombicuboctahedron’s edges.”13. It is noteworthy that the quantity of 64 is found in numerous systems in the cosmos, including the 64 codons in our DNA, the 64 hexagrams of the I Ching (Chinese Book of Changes), the 64 tantric arts of the Kama Sutra, as well as in the Mayan Calendar’s underlying structure.”9. Credit: Fine Mineral Photography by Laszlo Kupi, http://cosmometry.net/vector-equilibrium-&-isotropic-vector-matrix, http://www.matematicasvisuales.com/english/html/geometry/rhombicdodecahedron/rhombicdodecahedron.html, https://en.wikipedia.org/wiki/Rhombic_dodecahedron, https://en.wikipedia.org/wiki/Truncated_cuboctahedron, https://en.wikipedia.org/wiki/Rhombicuboctahedron, https://en.wikipedia.org/wiki/Deltoidal_icositetrahedron. It is also called the small rhombicuboctahedron. The plural can be either "icosahedra" or "icosahedrons". It starts with the tetrahedron and its dual (star tetrahedron). With D3d symmetry, it can be seen as an elongated trigonal trapezohedron. It can be seen as a cuboctahedron with square pyramids augmented on the top and bottom. From MathWorld--A Wolfram Web Resource. Those rhombi
Let's start with FOG. This is analogous to the dissection of a regular hexagon dissected into rhombi, and tiled in the plane as a rhombille. The triangles and squares share the same vector (side) length.
As such it is face-transitive but with irregular face polygons. The shape reflects balanced polarity (upward and downward pointing tetrahedra). Triangle FOX is right by construction, therefore,
It has 13 vertices, 24 edges, and 13 faces. Now we can get to some important data, that is, the relationship between the The rhombic dodecahedron is a zonohedron. is
If you build a model of the rhombic dodecahedron with the Zometool you will see exterior ones! face. It is the degenerate truncation (rectification) of both the cube and octahedron. Figure 4 -- showing the dihedral angle in simplified fashion, Now, EX and EY are known. To obtain EG, simply re-do the calculation we did previously. This page was last modified on 22 October 2015, at 12:52. It is composed of 8 tetrahedra pointing inward to one central point, alternating with 6 octahedra cut in half (3 total octahedra).
The rhombic dodecahedron is one of the nine edge-transitive convex polyhedra, the others being the five Platonic solids, the cuboctahedron, the icosidodecahedron and the rhombic triacontahedron. This animation shows the construction of a rhombic dodecahedron from a cube, by inverting the center-face-pyramids of a cube. It is the rectification of the great stellated dodecahedron and the great icosahedron. The cross-section of a rhombic dodecahedron is a hexagon. These are the stellated cuboctahedron, the truncated cuboctahedron and the rhombicuboctahedron. Recall that cantellation means truncating the edges. A rhombic dodecahedron appears in the … is a vertex, mid-edge and mid-face. Both triangles are congruent p. 130; Steinhaus 1999, p. 185). The rhombic dodecahedron is not a regular solid, because its facets are not regular, and it has three meeting at some vertices and four at others. The rhombic dodecahedron forms the maximal cross-section of a 24-cell, and also forms the hull of its vertex-first parallel projection into three dimensions. Each rhombic dodecahedron has the volume of a black cube and a white cube, or twice the volume of one of the original cubes.
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