24-cell

The octagonal projection of the regular 24-cell (3,4,3} reveals that the 24 vertices of this 4-dimensional polytope can be distributed as 16 + 8: the 16 vertices of the 4-cube γ₄ = {4,3,3} and the 8 vertices of its dual, the 16-cell β₄ = {3,3,4}. This view of the 24-cell is less well-known than the dodecagonal projection, in which the β₄ appears as two squares of different sizes joined by 8 equilateral triangles.