Twelve regular pentagons on thirty edges, three meeting at each vertex. Plato does not give it an element: he says the fifth construction was used for the whole, to embroider the universe with figures. The tradition afterwards filled the gap with aether, or with the zodiac, since the faces are twelve and five-sided. It is the solid of the whole rather than of a part.
Sacred Ratio
phi (its faces are regular pentagons, and a face diagonal is phi times its side)
Construction
Twelve regular pentagons folded three to a corner. Euclid constructs it inscribed in a sphere at Elements XIII.17, the last construction of the Elements, and the pentagon brings the extreme and mean ratio in with it. It is the dual of the icosahedron.