What type of hole is formed by a planar triangle of touching spheres?

To understand why a tetrahedral hole is formed by a planar triangle of touching spheres, consider the arrangement of the spheres. When three spheres are in contact, they define a triangular region between them. This arrangement results in a geometry that can accommodate another sphere positioned above or below the plane formed by the three spheres.

In crystal lattice structures, tetrahedral holes are created when there are four points that outline the vertices of a tetrahedron, with one point situated within the void created by the other three vertices. When looking at the triangle formed by the centers of the three touching spheres in our scenario, it is possible to visualize the apex of a tetrahedron as the additional sphere that can fit in the space above or below the plane of the triangle, effectively creating a tetrahedral void.

The nature of this arrangement leads to an effective packing arrangement where each sphere touches two neighbors in the plane and also has the capacity to accommodate additional spheres in the tetrahedral voids above or below, thereby maximizing the use of space in the structure.

In contrast, octahedral and cubic holes involve different arrangements and geometries, specifically relating to four or eight spheres in conjunction respectively, while a hexagonal hole relates to a planar arrangement involving more complex geometrical relationships, not