A 3x3x3 that can only do 180 degree turns on all faces has already been made by Hidetoshi Takeji and a variant is for sale in Oskar's Shop. A variant where only one axis allows 90 degree turns has also been made.
However, the remaining variant where only one axis is constrained to 180 degree turns has not been made yet. It was of course Andreas Nortmann's request to make one.
This puzzle represents a unique challenge in it's design: the half turn only cube can be made by bandaging a 7x7x7 and the one which is constrained on two axes can be made from a 5x5x5. This can also be seen as using different proportions for the cuts of each axis. However, the variant where only one axis is limited can not be made this way because the moment you make just the cuts of one axis disproportional two axes are instantly limited.
My solution is to work from the centerpieces, adding internal parts that block illegal turns. This mechanism could be used to construct many other puzzles, like a Helicopter Cube that does not jumble.
If you order this model, you will get a DIY kit of the plastic parts needed to make this puzzle. You will need to supply your own screws (M3), stickers and springs for assembly.
You can also order an assembled copy of this puzzle from me directly, but this option is more expensive and it will take longer to get your puzzle.
Shapeways has recently changed their pricing making this model much more expensive. I've not yet had the time to optimize this model to be as cheap as posible. Please contact me at firstname.lastname@example.org if you are interested in obtaining this puzzle so we can discuss cheaper options.