Here is my latest mod, the Master Skewb Kite.
The base is a LanLan Master Skewb, I extended and capped the puzzle with 1mm ABS plastic to the rhombic dodecahedron shape. The concept Skewb Kite is of course that of Tony Fisher's.
Here are the pictures (I won't be making a video, sorry):
A different angle
Yet another angle
A 60 degree turn still remains it in the rhombic dodecahedron shape
Size comparison with the Skewb Kite
The base puzzle