Message #3847

From: Melinda Green <>
Subject: Re: [MC4D] Melinda’s 2x2x2x2 solved
Date: Mon, 27 Nov 2017 17:51:19 -0800

First off, huge congratulations, Bob! I’ve been surprised by how difficult this puzzle turned out to be since the MC4D version is not considered to be terribly difficult. I knew you could do it, and I’m very happy to see a first solution. I’m looking forward to seeing optimizations, other solutions, and eventually speed solving contests.

On 11/27/2017 12:26 PM, Bob Hearn [4D_Cubing] wrote:
> […]
> For me the most interesting thing about Melinda’s 2x2x2x2 is that it exists at all. It seems kind of a miraculous accident. I wondered what the equivalent 2d representation of a 2x2x2 would be, and realized that it doesn’t exist, because squares do not have 3-fold rotational symmetry. We luck out here that the tetrahedral group is a subgroup of the octahedral group. I.e., that you can get the required 4-fold isotropic symmetry in a cube. Likewise, you can’t make a similar 3x3x3x3 — the three-facet pieces can’t be instantiated as cubes.

I’m as surprised as anyone. A lot of things had to fall into place for this to happen. Even after coming up with a workable design it was still years before I had a mechanism that could implement it. Perhaps the final piece was finding a usable whole puzzle reorientation. Yes, the real accident is the relationship between the cube and tetrahedron in 3D. I expect this will be the cause of endless objections when people assume I’m making a huge error in thinking that my 3D cubes have some shape relationship with 4D cubies which they definitely do not.

> So what kinds of 4d puzzles can be implemented this way? Is this it?

You mean by using cubes? That’s a new and interesting question. I have no idea!