I decided to do a spoiler write-up on Convolution: http://gladhoboexpress.blogspot.ca/2013/02/a-mathematically-crippling-deform... While I described (hopefully accurately) all the action, I did not actually engage the mathematics (D is piece #2 in the previously mentioned John Rausch picture): "… two points: A at (2,1) and B at (3,2). Now, the 'rotation': What happens is that A slides along y=1 toward the right while, at the same time, B slides along x=3 toward the top. How long is the slide? Somewhere between D's line x=3 reaching the point (4,1) and D's corner (4,2) reaching the line y=3. Within this range, piece D may be removed by lifting it up the z-axis. What happens to the line (2,2)-(2,3) during this movement? It slightly ablates the upper-right quadrant at (2,2) ..." On Feb 21, 2013, I wrote:

Bill Gosper's sharing of the 4x4 "nice little sliding block head exercise" got me thinking about Stewart Coffin's 4x4x4 Convolution puzzle. John Rausch shares a partially assembled Convolution on his Puzzle World website:

http://www.johnrausch.com/puzzleworld/puz/img/lg/convolution_6.jpg

Three pieces (#1 at 9 o'clock, #2 at 7 o'clock, #3 at 5 o'clock) need to be added to the assemblage. The black 'cubies' end up in the corners of the finished cube. Also, piece #1 and piece #3 are seriously foreshortened (what look like one-cubie extensions going to the back are actually two-cubie extensions). The number of cubies in each of the three unassembled pieces is 9 (to fit into the 27 empty spaces of the unfinished cube). Can you complete the construction in your head?

Bonus: What's wrong with one of the cubies?