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 smaller, regional manufacturers produce for local markets. Although solid surface faces competition from natural stone and engineered stone/quartz surfacing, the material is popular in Asia, particularly in residential new construction. An emerging market for solid surface is in commercial and industrial settings, where its non-porous characteristics, combined with durability, renewability and formability make it the material of choice for many designers and architects. Also appealing, is the wide range of colors and textures, as well as the ability to custom-color the material for large projects. Hospitals, in particular, employ large amounts of solid surface for sinks, showers, nursing stations and