Behold! The MBTI tesseract! While bringing nothing new in terms of typology, this is an excellent way to visualize the interplay between types!
All 16 types reside on 1 4cube.
There is 1 4cube.
Each 4cube contains 16 vertices (types).
Each vertex straddles 1 4cube.
Within the 4cube each letter is a 3cube (some, of course, distorted because of the projection from 4D onto 3D... onto 2D). There are (surprise!) 8 3cubes.
There are 8 3cubes.
Each 3cube contains 8 vertices.
Each vertex straddles 4 3cubes.
The boundaries between two cubes form a 4-vertex 2square. There are
24 2squares. Four of these represent the traditional temperaments, NT, NF, SJ, SP. However, each possible combination of two letters is a square, and it's a given that each face is a set of shared properties. Other common faces I've seen referred to were IP, IN, NP, and so on.
There are 24 2squares.
Each square contains 4 vertices.
Each vertex straddles 6 2squares.
Finally comes perhaps the least important layer of distinction, the 1line. there are 32 1lines. On each 1line are two types sharing three letters. In terms of the functions the vast majority of 1lines will have little significant in common aside from a three-letter similarity.
There are 32 1lines.
Each 1line contains 2 vertices.
Each vertex straddles 4 1lines.
I'm sure I could babble on more about this and I was intending to place this whole thing in Cartesian 4-space and play around with that but I'm lazy. Additionally, I was planning on making clearer diagrams as well as seeing how the functions work under various transformations but it's a lot easier to just say "I was going to do it" than to do it.
P.S. I probably will add more later.