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 such as metal alloys or polymers. Solid surfaces are synthetic surfaces manufactured from polymeric materials. Tools of surface fabrication include routers, drills, templates, clamps, ovens, suction cup grips, and table saws. Larger surface fabricators may also use CNC routers. For all but the simplest jobs, surface fabrication usually takes place in the workshop, after which the finished product is assembled and installed at the work site. Installation of multi-part surfaces, such as "L" and "U" shaped countertops, often involves complex work with specialized tools, to create a seamless result. Solid surfaces is used in the following environment : Solid surface