Customized Rubik's Cubes

My friend Kristin Looney has developed Custom Cube Technology -- tools for putting new designs on Rubik's Cubes. I saw a bunch of her creations. Immediately, my eyes crossed, my brain started bubbling out my ears, and I began sketching notes for my own patterns.

Oddmaze

Plan #1 is a maze; or rather a labyrinth, since there are no branches or dead ends.

Note that each face has a different symbol in the center, and the symbols are orientable -- you can tell which way is up. (The small "Z" signature on each face also helps orient the faces.)

The patterns look random, and to a certain extent they are. But I did give some thought to the layout. There are six possible edge patterns, and each one appears exactly twice. There are ten possible corner patterns, but two are mirror images and one has a tiny loop which can never be joined to any other path; that leaves eight usable distinct patterns, each of which appears exactly once.

The layout shown above has more nice features. It has the Celtic knotwork property: when following any path, you always alternate crossing overpasses and underpasses. (The symbol-node at the center of each face does count as a crossing.) Also, the six pairs of identical edge cubes are never either on the same face nor exactly antipodal to each other.

There are a number of different challenges with this cube.

• Mix the cube around, then get from one face-symbol to the opposite face. (You must actually reach the symbol on the path it's on, not the one that crosses underneath it.) This is actually more likely than not to happen by pure luck. But if it doesn't, try to create such a path in a few cube moves as possible.
• Make nice symmetrical patterns on every face. (Probably difficult, but depends on how aesthetic you want to be.)
• Since there are no branches or dead ends, the paths always form some number of closed loops. Try to make a loop that crosses every one of the 54 squares at least once.
• Try to move all the paths into a single loop. (Accomplished by Jake Davenport.)
• Produce the Celtic knotwork property (see above). This is possible, since I designed it that way; the pattern shown above has this property. But it's very difficult.

Colorspace

This isn't logically any different from the standard Cube -- except that the centers of each face have to be oriented correctly. However, it sure does look cool, doesn't it?

Necker Cubes

Again, a standard Cube puzzle. Comes with built-in migraine. Each face has a different arrangement of the three colors (light, medium, dark), although the patterns (before coloring) are identical. Then the three colors are made by varying widths of dark brown lines on light tan. So there's only one solution, but you have to squint to have any idea what's going on.

The effect is deliberately reminiscent of an Escher woodcut -- both in design and shading.

House of Stairs

This is another interesting one. The stairs go up and down, through gaps in the railings and openings in the platforms themselves. The perspective is rather inconsistent; the stairs appear to slant the way perspective says they should, but the platforms are all at the same altitude.

There are two levels of challenge here:

• Make the stairways consistent, so that every one has an "up" end and a "down" end. Make sure no two "ups" meet at a border, or two "downs".
• Make the stairways consistent, as above, and also make the entire cube consistent. There should be no impossible loops, where you can go down and down and down and return to your starting point. This is known to be possible, since I designed the original pattern to have this property. But there's almost certainly only one way to do it, and it's probably only possible to reach it by looking at a diagram of how it should look. (I think this is a flaw; it would be more fun if it were actually easier, so that you could do it without a diagram.)

The Cube of Quendor

This is pure nostalgia. Each face has a segment of the map from one of six Infocom games (Zork 1, Zork 2, Zork 3, Sorcerer, Spellbreaker, and Beyond Zork). Significant features of the landscapes are represented. You may also note the compass, the brass lantern, and the rare Quendorian Compass Rose.

The idea for this comes, obviously, from my own obsession with text adventures.

The paths don't match up between the faces, which is rather a pity. I was choosing map pieces to be individually appropriate -- not to fit together. (This flaw is fixed in the Colossal Cube, which is shown below.)

All these games are in print from Activision, on their Classic Text Adventure Masterpieces of Infocom collection CD (for Mac and PC). In addition, Zork 1, 2, and 3 can be downloaded for free from Activision's web site (Win95 only). I think they're at ftp://ftp.activision.com/activision/zork1/demo/, and similarly zork2 and zork3; or possibly ftp://ftp.activision.com/zork/legacy/. But I haven't been able to get in to check.

"Listen"

An experiment in blank verse. Or, if you prefer, refrigerator-magnet poetry.

The outer bands, in the original configuration, read:

• Alice fell through the hole, but never feared what was there;
• we all leaped up to the stars, and got lost in the void beyond;
• they crawled out of the sea, and we fled from the sight weeping;
• I turned from their eyes, for I never knew the burden bound there;
• you and I ran towards the way out, but could not see what lay ahead;
• no one waited for the end, but all fell to their fate at last;
• sing these words but tell them true and
• twist my ideas to make them clear and
• take six poems and turn them round but
• shut your eyes and hear my hopes and
• take no paths but see all ways and
• spare those pains and mean these ends and
As you see, the lines lack capital letters and final punctuation, so each one loops forever.

The sentence structures are parallel, so swapping around analogous parts of different faces gives grammatical results (I won't go so far as to say "meaningful". Heh.) Unfortunately, the group of cube rotations does more than swapping analogous parts. A scrambled cube is generally nonsensical. The challenge is to make one or all sides read nicely. This is as difficult or easy as suits your sense of poetic obscurity.

Earthcubes

Once upon a time, in a high school far far away -- Walter Johnson H.S. in Rockville, I believe -- I saw these twelve posters hanging on a classroom wall. Each showed a fantastical distortion of the Earth, along with a gnomic phrase. "What if the Earth were... Toroidal? The North Pole coalesces on the South Pole at the inner equator for achieving ultimate cool."

These Earthshapes were designed by Joseph N. Portney. I finally found them on the web site linked above; and I thought, well, hey, twelve of them. So I made two cubes.

(The Earthshapes are copyrighted by Litton Systems, Inc. The Terms of Use on their web site say: "Material displayed on the Site may be downloaded for non-commercial, personal use only, provided you also retain all copyright and other proprietary notices contained on the materials." Those are the terms under which I created these cube patterns.)

The Colossal Cube

Companion to the Cube of Quendor. This is a single contiguous segment of the Colossal Cave map, wrapped around all six faces. It was, you should pardon the expression, a bear to design. (I sketched six or eight combinations of map variations before I settled on this one.)

The detail is a little fuzzy on the image on this page. But if you look carefully, you can find three living creatures, nine treasures, two signs, a mirror, two chasms, a crack barely wide enough to squeeze through, and a twisty maze of passages, all different.

The map is almost perfectly correct, as far as it extends. One path is shown going east from a room instead of down, but that's the single error. You'll note that I had to rotate a few squares to make their paths match up. The twisty maze is also rather stylized, but it is topologically correct; eleven rooms all connected to each other, except for the dead end with the battery vending machine.

Three magic words could have been noted on the cube, but I couldn't think of a really good representation, and then I forgot. Oops.

Liquid Crystal Cube

I pretty much got out of the custom-cube business last year (1998), because I moved away from DC and couldn't use Kristin's die-cutting jig every week. But I had this one evil thought, and it was worth going to DC just to make the cubes. (Well, also to visit people.)

The thought is simple: Go look in an Edmund Scientific catalog. They sell thermosensitive liquid-crystal sheet -- the stuff that changes color when it gets warm.

They sell six different grades of it. Each grade changes color (black to red to green to blue) in a different temperature range. The lowest is greenish at room temperature; the highest doesn't change color unless you hold it near a light bulb.

Enough said?

Earthshapes were created by Joseph Portney and are copyrighted by Litton Systems, Inc.

The other cube patterns and the diagrams of them on this page were created by me. They are copyright 1998-9 by Andrew Plotkin.

The photographs of the completed cubes were taken by Andy Looney. They are used here by permission.

Last updated May 10, 1999.