The fifth regular polyhedron, the dodecahedron , was left over, so Plato proposed rather lamely that the god used it up for decorating the universe.
As well as constructions to divide a line in the golden ratio, Euclid gives applications such as the construction of a regular pentagon, an icosahedron and a dodecahedron .
Dali also incorporated in the painting a huge dodecahedron (a twelve-faced Platonic solid in which each side is a pentagon) engulfing the supper table.
There is a fifth Platonic regular solid too: the dodecahedron , which has pentagonal (five-sided) faces.
Finally, so as not to leave out the one remaining regular solid, he proposed that the dodecahedron represented the shape of the entire universe.
Grossular occurred as greenish-gray to pale brown semitransparent dodecahedral crystals to 8 mm and also as a granular material making up a high percentage of the skarn.
Sphalerite is cubic with crystals commonly tetrahedral or dodecahedral and frequently complex and distorted.
Archaeologists have unearthed models of dodecahedra at several sites in Europe, including a dodecahedral model in Germany that had holes of different sizes puncturing its faces.
Fluorite from Dongshan occurs only as simple cubes consistently modified by small dodecahedral faces.
They described a distorted 5.5 x 4-cm dodecahedral crystal of genthelvite from a small pegmatite near Stove Mountain.