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^{[1]} 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.

Simplicial polyhedra include:

- Bipyramids
- Gyroelongated bipyramids
- Deltahedra (equilateral triangles)
- Catalan solids:

Simplicial tilings:

- Regular:
- Laves tilings:

Simplicial 4-polytopes include:

Simplicial higher polytope families:

- simplex
- cross-polytope (Orthoplex)

**^**Polyhedra, Peter R. Cromwell, 1997. (p.341)

- Cromwell, Peter R. (1997).
*Polyhedra*. Cambridge University Press. ISBN 0-521-66405-5.