Smallest non-4-space-filling polytesseract? As a follow-up to Smallest non-space-filling polycube?, what's the smallest polychoron produced by fusing tesseracts 3-face to 3-face which does not fill 4-space?
 A: Looks like the smallest polytesseract not able to fill 4-space has to be at least a decatesseract, possibly larger! either an undecatesseract or a dodecatesseract (updated after Edit 2)!
I updated my code in github: whuts-solver to make it work in higher dimensions (and optimized it to run much faster), and tried generating tilings with polytesseracts in the last couple days.
So far, it looks like there exists a 4d-space-filling tiling for all polytesseracts up to and including nonotesseractsdecatesseracts! The individual results are in the github link in results/poly_4_x.
I am now running the code for all decatesseracts, but this is running much slower, after one day it has processed around 50,000 of the around 850,000 possible decatesseracts (found a tiling for all of those so far). I will update when that run finishes, but looks like this will take some time...
I could indeed have ignored the ones that get produced by elevating a polycube (except the ones that don't tile 3d-space), but this is a small percentage anyway, so I just let my code run on all beginning from pentatesseracts.
Edit
I came up with a dodecatesseract, which definitely does not tile 4-space (elevating the image below into 4d). Nothing would fit in the "hole" in the middle. That means, if my search through the decatesseracts finds a tiling for all of them (it is now around half way through and so far all work), the smallest non-4-space-filling polytesseract would be either an undecatesseract or a dodecatesseract. There are around 9 million undecatesseracts, so checking those would take quite some time. I did check the ones that get generated by removing one hypercube from the dodecatesseract in the picture (I thought if anything, these would be difficult to fill 4-space), and those can fill 4-space. Also, I run some code to check all undecatesseracts, whether there is any that obviously does not tile space, similar to the dodecatesseract (with a hole that can not be covered), but it looks there is none such.
Edit 2
My code finished running for all decatesseracts and found a 4-space filling tiling for each of them! I put all tilings in one file in my github under results/poly_4_10_all.json.bz (one big json file compressed with bzip2, containing a list of solution in the format previously used).

