16-cell

Definitions

A four-dimensional polytope, analogous to an octahedron, whose sixteen bounding facets are tetrahedra.

Equivalents

Examples

“The remaining 8, as before, are the vertices of the complementary 16-cell (see⟳ Figure⟳ 9). In Figure⟳ 7, these 8 points have⟳ been blackened, but not joined, because the 16-cell has longer edges; diameters of octahedral facets of the 24-cell.”

“This polytope has 16 tetrahedral cells, and for this reason⟳ it is called the 16-cell.[…]The 16-cell has 24 edges that are the diagonals of the 24 square faces of the hypercube. (Since we are selecting alternate vertices of the hypercube, we only get⟳ one diagonal for each square face⟳.)”

“We will now consider⟳ the dual 16-cell. In some ways the 16-cell is a bit easier because it has fewer vertices and edges. But on the other hand the hypercube is perhaps easier to understand⟳ intuitively because we can readily (perhaps) see⟳ the various cubes of which it is composed.”

CEFR level