I have a relatively simple question: are there different names for a cube in different poses?
Specifically, I need to distinguish a regular cube (i.e. a cube lying flat in the XY plane and parallel to the X and Y axes) from a tilted cube (i.e. rotated so that two vertices are vertically co-linear and the cube now forms a kind of diamond shape side on).
The closest thing I could find is on Wikipedia where it seems to suggest that the first is called a 'Regular hexahedron' and the second may be called a 'Trigonal trapezohedron': https://en.wikipedia.org/wiki/Cube
But I'm not sure if this is correct or if there is not a better terminology out there... perhaps in crystallography?
Any help would be very much appreciated,
Rod.
Well, when considering the axial arrangement, then you could indeed distinguish between the square prism and the trigonal trapezohedron. But, as already pointed out in the comment, those shapes then are no longer restricted to the regular cube only, rather would well suit any scaling within that special z direction.
Thus you would probably have to resort to attributions somehow. - Whether you'd like to distinguish between the "cubical version of the square prism" vs. the "cubical version of the trigonal trapezohedron" or rather would like to use terms like "face-standing cube" vs. "vertex-standing cube" or else could distinguisch "face-2-face oriented cube" vs. "body-diagonally oriented cube" is then more a matter of taste.
Btw. your quest forget about the further possible orientation, the "edge-2-edge oriented cube", q.e. the "cubical version of the rhomb prism" or "edge-standing cube".
--- rk