Platonic solid to that of a sphere of the same size (i.e. either the same surface area or the same volume.) The dodecahedron, on the other hand, has the smallest angular defect, the largest vertex solid angle, and it fills out its circumscribed sphere the most. Every polyhedron has a dual (or "polar") polyhedron with faces and vertices interchanged. The dual of every Platonic solid is another Platonic solid, so that we can arrange the five solids into dual pairs. If a polyhedron has Schläfli symbol {"p", "q"}, then its dual has the symbol {"q", "p"}. Indeed, every combinatorial property of one
Solid surface manufactured in sheet form for fabrication into finished countertops, solid surface can also be cast into a variety of shapes, including sinks, shower pans and bathtubs. Sheet goods can also be heated and bent into three-dimensional shapes using a process called thermoforming, which adds to the versatility of the product. Color and design flexibility are key factors when choosing engineered composites over natural stone. In a residential setting, solid surface can be used as kitchen countertops, bathroom vanity tops, and shower and tub surrounds. Countertop fabricators typically join solid surface sheets into desired shapes using a two-part adhesive, after which