The dissection of a rhombic triacontahedron interior into 10 obtuse and 10 acute hexahedral "rhombs" --- sheared cubes, with face diagonals in the golden ratio --- is well-known, apparently going back to Kepler. (A) Modulo symmetries of the icosahedron, is the dissection unique? (B) How many isomorphic solutions are there? George Hart introduces an elegant 5-colouring of the rhombic faces: see http://www.georgehart.com/virtual-polyhedra/dissection-rt.html. (C) Does 5-colouring rhombs make the dissection easier? harder? It is elementary that the triacontahedron exterior has 30 faces, 60 edges, 32 corners; Coxeter (Regular Polytopes, sect 2.71 p26) asserts that 21 faces belong to 7 obtuse rhombs, and 9 to 9 acute rhombs. (D) How many more (non-coincident) corners, edges, faces, solids are hidden in the dissected interior? Guy Inchbald has a page showing some exploded views of the dissection: see http://www.steelpillow.com/polyhedra/quasicr/quasicr.htm These are difficult to interpret, largely as a result of the tendency of (technically oriented) human vision to re-interpret perspective rhombs as (weirdly oriented) rectangles. I have prepared a Maple worksheet which allows the exploded dissection to be colour-coded, rotated interactively, and (with some difficulty) selectively dis-assembled; the results are notably easier to interpret. The script is available on email request. Fred Lunnon