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 the cured joint is machined flat. The same method is used to build up edge thickness, which can be profiled using tools and techniques similar to those used to work hardwoods. A major appeal of solid surface is its impermeability. Solid surface sinks can be joined to the countertop surface with no gaps, which eliminates areas for water to collect and bacteria to grow. Integral backsplashes can also be created that follow the contours of the wall “seamlessly” and without gaps. Should the material become scratched or broken, solid surface can, in most cases, be repaired quickly by a certified