Hello,

I recently learned about Euclid and The Elements. Inspired, I went on a geometry rampage. A sad little 2x2x2 got in my way and this was the result. Incidentally, as I have recently begun expanding my collection into non-twisties, I feel less 'attached' to my twisty puzzles and as such some of them may find themselves being hacked apart to support such mathematical madness.

This is my first attempt at using sheet plastic for capping purposes. It is a 2x2x2 cut along lines drawn from halfway on two adjacent faces to the corner closest to the two of them, then rotated along a vertical axis by 180 degrees to create an interesting shape. It has 10 faces: 2 in the shape of parallelograms, 6 in the shape of isosceles triangles (of varying sizes), and 2 in the shape of irregular pentagons.

This puzzle was constructed from a Rubik's 2x2x2 using a Dremel cutting wheel, plastic sheeting, superglue, Apoxie Sculpt, and acrylic paint. As this was also my first attempt at using the Dremel, I cut irregularly in some places and the use of the sanding wheel left me with large gouges that needed to be sanded down and fixed up. That said, my sanding job was quite nice and I was left with faces that are smooth but incorrectly shaped. It looks like that will be the trade-off until I develop my skills further. I also botched the stickers and ran out of material (though I did use my 'trademark' pearl stickers).

This project has led me to two issues to be addressed: firstly, what solids can be made within the confines of a 2x2x2 or 3x3x3 mechanism that can be realized solely through truncation?

The second is the suggestion that, like the other puzzle forum(s), we have a subforum dedicated to math.

Photos:

Your first question can't be answered without restricting truncations into specific patterns.
Without such restrictions truncating a corner by 9mm*10mm*11mm is something different compared with truncating a corner by 10mm*10mm*10mm. What restriction do you want to apply?

For questions about puzzle-related math there is the "General topics"-forum. I suspect that another forum will be ignored even more than that forum.

Regarding the shape:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=1853

My restriction is...geometry . Your two cases would produce what is essentially the same shape. I'm not sure how to get more technical than that though. You seem to be well on your way to answering that question with your quest to make every mod in existence though (you deserve more mad props for those, by the way-I never realized exactly how cool those are until I saw that one curvy copter transformation at IPP)

I've been watching this one over on Facebook. Nicely done!