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If you look carefully, the solids that aren't regions are actually octahedrons. There's no corner opposite the triangles in those directions.
Right! And if you look even more carefully, aside from tetrahedron regions and octohedra, there is a single extra upside down tetrahedron that is not technically a region, but effectively is one.
Does that last digit count as a 3 in the corner?
Secret bonus of 3d I suppose, you can fit more than two 3s in corners!
If you look carefully, the solids that aren't regions are actually octahedrons. There's no corner opposite the triangles in those directions.
Right! And if you look even more carefully, aside from tetrahedron regions and octohedra, there is a single extra upside down tetrahedron that is not technically a region, but effectively is one.
Does that last digit count as a 3 in the corner?
Secret bonus of 3d I suppose, you can fit more than two 3s in corners!