I have found an other missing piece, the ten color Diamond cube, also refer to as small rhombi-cubo-octahedron. In Cubic Circular 3&4 there are two diamond cube described the 3 color and the 10 color.



In cubic curcular there are many puzzle variation described, it is a great source for information about (rare) puzzles

See more on Jaap's site
Cubic Circular 1

Cubic Circular 3&4

Ton

Can this be called "rhombi"? No part of the puzzle shows a rhombic shape unless I'm forgetting something.

It's because the faces lie in the same planes as those of a rhombic dodecahedron, a cube, and an octahedron.