High Quality Content by WIKIPEDIA articles! In geometry, a simplicial polytope is a d-polytope whose facets are all simplicies. For example, a simplicial polyhedron contains only triangular faces and corresponds via Steinitz's theorem to a maximal planar graph. They are topologically dual to simple polytopes. Polytopes which are both simple and simplicial are either simplices or two-dimensional polygons.In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on in higher dimensions (such as a polychoron in four dimensions). Some theories further generalise the idea to include such things as unbounded polytopes (apeirotopes and tessellations), and abstract polytopes).

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