29 June 2007
I'll finish the week with one final pattern that shows that Octahedron patterns don't have to be so complicated-looking.
Each face shows an hourglass, resembling the markings on a black window spider. It's a natural shape for this kind of puzzle, and it can probably be done a few different ways. As shown in the end-view at right, each "hourglass" pairs a mobile edge piece with a non-mobile center piece without involving any corner pieces.
27 June 2007
That title is a real mouthful, isn't it?
Each face has a three-color triquetra arrangement, but unlike the previous Octahedron Triquetra each face is a mirror-image of each of its three neighbors. As a result, four faces show a left-handed triquetra and the other four faces show a right-handed triquetra. This arrangement resolves the agnostic edge, something that wouldn't be possible in a Pyraminx Triquetra pattern.
Of the platonic solids, only an 8-sided puzzle can divide the puzzle into two schemes where each face uses a different scheme from all of its neighbors. An ordinary Rubik's Cube can't do it. The Skewb Diamond (a different octahedron puzzle) can get half solved, so that each solved face was surrounded by three unsolved ones.
24 June 2007
Each face in this Magic Octahedron pattern looks like the previous Pyraminx Gale Warning, except that I inadvertently flipped it (mirror image).
Any pattern a Pyraminx can do, it seems an Octahedron can do better.
But don't assume the Octahedron is limited to the relatively mundane patterns as the Pyraminx puzzle. At first the Octahedron struck me as a Pyraminx, just with twice as many faces, twice as many corners, and twice as many edges. But I've begun to discover that it can do a lot more than this. More soon...
23 June 2007
In coastal areas you'll sometimes see a Gale Warning signal, a pair of triangular red pennants flying one above the other as illustrated at right.
This pattern simulates the gale warning three times on each side in three different colors. It's an imperfect imitation, but the pattern itself is interesting because it pairs a mobile edge piece with a non-mobile tip piece without tying them to the immobile center piece between them. (Like the tips, the center pieces can only rotate around the corner they're connected to.)
17 June 2007
Although similar in appearance to the Quad-color Python, this pattern is infinitely easier to construct because there are dozens of possible solutions.
This is essentially a standard snake pattern extended to the 5x5x5 by permuting each of the three stripes differently to yield four colors per face.
11 June 2007
Possibly the simplest pattern for the even-numbered cubes, Pinstripes requires only 4 moves on a 2x2x2 and only 8 moves on a 4x4x4. Only 12 moves would be required on a 6x6x6 cube.
A similar-looking pattern can be arranged on the 5x5x5, but it's based on a different principle.
05 June 2007
Geometrically speaking, a triskelion is a three-armed spiral form. In heraldry (flags that is) it instead refers to a three-legged spiral such as the flag of the Isle of Man.
The pattern extends neatly to any higher-order puzzle cube in case you just happen to have a 9x9x9 cube lying around. Here's the opposite-side view:
01 June 2007
This spring-shape looks a lot like a 3-cycle rotation, but it's really an opposite-face pattern. For an opposite-face pattern, it employs the bare minimum number of edge cubies of each type (other than none).
Some faces use odd numbered quantities of center-edge and center-corner cubies, adding a little complexity to what would otherwise be an easy beginner's pattern. Just a little.