Word of the week:     Polytope

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). 

When referring to an n-dimensional generalization, the term n-polytope is used. 

For example, a polygon is a 2-polytope, a polyhedron is a 3-polytope, and a polychoron is a 4-polytope.

The term was coined by the mathematician Hoppe, writing in German, 

and was later introduced to English mathematicians by Alicia Boole Stott, the daughter of logician George Boole.

(From Wikipedia)

Graphs of six convex regular 4-polytopes

4-simplex (5-cell)	4-orthoplex (16-cell)	4-cube (8-cell, Tesseract)
24-cell	120-cell