The regular tetrahedron can't tessellate the space
If we dispose 5 regular tetrahedra around an edge, we don't get a bipyramid with pentagonal base: there will be a small hole because the dihedral angle of the regular tetrahedron is less than 360°/5. We can't tessellate the space using only regular tetrahedra.
© matematita
The image belongs to the sections...:
Prisms, antiprisms, pyramids, dipyramids (3D geometry)
