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.

Source: wiktionary

2002, T. Robbin, Formian for art and mathematics, G. A. R. Parke, P. Disney (editors), Space Structures 5, Proceedings of the 5th International Conference on Space Structures, Volume 1, page 445, One more example of a four dimensional tessellation is given using the 24-cell, see Fig 2.

Source: wiktionary

The regular polytope with Schläfli symbol {3,4,3}, the so-called 24-cell, can be obtained from the 16-cell as follows. The vertices of the 24-cell are the midpoints of the 24 edges of the 16-cell.

Source: wiktionary