Idea of this puzzle is simple and I'm sure there are some who already had it before, but I have never seen it physically realized.
This is a Skewb with two-fold stretched "face square" and with four additional dino-cuts. Like a Master Skewb, it has 3x3x3x3 cuts system, but each one cutting layer of a pair is moved so it cuts vertices, thus reducing the number of elements and making the puzzle much easier to solve.
Mathematically it can also be considered as a TomZ's Dino Skewb that is bandaged over half of all face diagonals.
On each face one can see a Cyrillic letter Ф (or Greek Phi) which is read as F, that's why I named it F-Skewb.