Pentagons and hexagons
If we take a tessellation in pentagons, we can group them in groups of 4 to form hexagons or in the way shown in the figure. Alternately, we can group them in this other way, that is, in a certain sense, "perpendicular" to the preceeding one. This observation plays an important role in the construction of the 120-cell (that is one of the 6 regular polytopes in dimension 4), and in the way in which we can paste together two solid tori of 60 dodecahedra each, that are contained in a 120-cell.
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120-cell (4D geometry)
