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In geometry, a simplicial polytope is a polytope whose facets are all simplices. For example, a simplicial polyhedron in three dimensions 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.

1. A simplicial polytope is a polytope in geometry where each facet is a simplice.
2. As an illustration, a simplicial polyhedron in three dimensions with only triangular faces corresponds to a maximum planar network according to Steinitz's theorem.
3. They are simple polytopes topological dual.
4. Two-dimensional polygons or simplices are polytopes that are both simple and simplicial.