Distinguishing between octahedral and tetrahedral holes
To visualize holes in closest packing of spheres, you need 6 balls (marbles, table tennis balls, etc) of equal size. 3D closest packing can be constructed from 2D layers of closest packed spheres as such:



The light blue layer is on the bottom and the dark blue layer is on top. The holes, tetrahedral or octahedral, are in between layers.

To find a tetrahedral hole, take three balls and arrange them in a triangle to form part of the lower layer. Then place one sphere in the center on top (you have to keep the lower level together somehow or the structure will collapse). Your tetrahedral hole is in the center of the tetrahedron formed by the 4 balls (marked T in the picture).

To find an octahedral hole, you need a helper or glue. Take three balls and arrange them in a triangle. Take another three balls and arrange them in a triangle. Place the two triangles on top of each other, twisted against each other by 60 degrees. This is a octahedron on its side, and in the center is the octahdral hole.

In the picture above, these positions are marked by T and O. You just have to imaging that they are in between the layers, and then you might be able to count nearest spheres. The picture below shows the arrangement of the nearest spheres, only.



If you don't have 6 balls handy, but have two hands handy, you can also do the following. Place thumb, pointer and middle finger together so that the finger tips form a triangle. Point at the center of the triangle with the pointer of the other hand. That's the tetrahedral hole. Now, form a triangle with the finger tips of your other hand. Bring the 6 finger tips together with a little twist so that they "lock in". At the center of the 6 finger tips, you have the octahedral hole.

So, whether you are a visual or a haptic learner (not that that would be a thing), this will do the trick, I hope.




  There are some images of octahedral and tetrahedral holes


Actually, I only found images of the spheres representing the atoms, no images of the shape of the space in between. If you squeeze some blue play dough between two layers of marbles, here is what you get (see also https://leancrew.com/all-this/2019/06/cheesegraters-and-crystals/): 



Within a layer, each indentation is surrounded by six others. The arrows point at the six locations with the largest voids (in the center of triangles formed by the sphere and two of its nearest neighbors in that layer). If you look closely, each indentation has three holes, the contacts with the layer below. The voids take on different shapes depending what is underneath. If a sphere is directly underneath, it is a tetrahedral hole. The shape of this is a tetrahedron with "dented in" faces (far right). If a center of a triangle is directly underneath, it is an octahedral hole. The shape of this is a cube with "dented in" faces (near right; cube and octahedron are complementary archimedian solids: the centers of the faces coincide with the other's vertices and vice versa. A tetrahedron is complementary to itself).

If you shrink the spheres around the atoms to points, you get a space-filling arrangement of tetrehedra and octahedra called a tetrahedral-octahedral honey comb.  

Teaching this material

Stefanie Lenzer, Bernd Smarsly and Nicole Graulich recently published a paper in J Chem Ed on using clear spheres to explore crystal packing and voids.