Image of a Cube, compressed or stretched in diagonal direction

Do you believe that these are views of the same object from different directions?
The faces are ALL congruent rhombi and certainly no parallelograms. The ratio of the diagonals of the rhombi is (sqrt(5)+1)/2 = 2/(sqrt(5)-1) -- hence "golden rhombi", see the last image on the page of the IcosiDodecahedron.
We got interested in this Rhombohedron because of non-lattice tilings. But we could not write good enough code to play with many of it on a screen and we did not get someone to make us a large collection of wooden pieces.
One can make two different rhombohedra from the rhombic faces. In the shown example we have two opposite vertices where three large angles meet and three pairs of opposite vertices where two small angles and one large angle meet.
The other rhombohedron case has two opposite vertices where three small angles meet.
The Rhombic Triacontahedron Puzzle consists of 10 pieces of each of the two and the task is to put them together to a triacontahedron.