Simple polytope

The family of polytopes which are both simple and simplicial are simplices or two-dimensional polygons.

In general, any polyhedron can be made into a simple one by truncating its vertices of valence four or higher.

Four-dimensional simple polytopes include the regular 120-cell and tesseract.

Micha Perles conjectured that a simple polytope is completely determined by its 1-skeleton; his conjecture was proven in 1987 by Roswitha Blind and Peter Mani-Levitska.

[3] Gil Kalai shortly after provided a simpler proof of this result based on the theory of unique sink orientations.