Octahedron Christmas Trees

Okay, there's nothing particularly Christmas-like about this pattern. It's just a vague depiction of a tree, but I chose to call it a Christmas Tree because of the season.

Woolworths used to sell decorations like this back in the 70's when abstract geometric shapes were the "in" thing.

Pyraminx Christmas and Hanukkah

This is a chance color scheme that appeared while I was toying with Meffert's 25th Anniversary Edition Metallized Pyriaminx. When the colors are permuted as shown the red-green sides suggest a Christmas color scheme while the gold-blue sides (roughly) suggest a Hanukkah color scheme.

The color scheme isn't a perfect match, but it's powerfully suggestive when holding the puzzle solved this way.

5x5 Curvy Snake

This is a 5x5 variant of the standard "snake" pattern from the 3x3 cube, but with curves added.

I made this pattern during a holiday in Hawaii and accidentally stumbled on the Tropical Petals pattern afterward. So the simplest way to create either of these patterns is to first arrange the edges as shown here for the Curvy Snake, then adjust the center pieces to match either the Curvy Snake or Tropical Petals pattern.

Octahedron Snow Angels

This shape was inspired by a traditional snow angel.

As usual, the design is somewhat abstract. But when working with a slate of nine triangles any patterns has got to be pretty abstract.

Broken Python

On the 4x4 this pattern looks a lot like a standard "python" pattern, except that the pattern has a beginning and an end instead of being a loop. On a 5x5 it's a little more obvious that the pattern itself IS a type of loop.

It's constructed like a standard python, but the pieces on one edge (the purple-white edge in this example) are swapped around to break the pattern.

5x5 Tropical Petals

This pattern occurred just by chance during my holiday in Hawaii. An Eastsheen cube naturally forms two groups of colors that look tropical: a red-yellow-blue scheme reminiscent of a tropical Macaw, and a white-purple-green scheme like an orchid.

The pattern itself is a variant of a standard snake, albeit with several modifications. The pictures were takent near Kona, Hawaii.

5x5 Grecian Urn 1

This pattern features two strings, one which weaves on-and-off the top of the cube and the other weaves on-and-off the bottom.

The picture doesn't make it entirely clear, so the schematic is shown at right.

Octahedron Tri-color Clover

The Magic Octahedron completes the set of Tri-color Clover patterns.

There are several different ways the pattern could be achieved on the Octahedron. This one uses opposite-face colors at each of the corners, equivalent to turning each of the corners one-half turn. Because there are eight corners, it can also be done by the equivalent of turned each corner a quarter turn.

Mastermorphix Tri-color Clover

Because of its triangular shape, it seems natural to re-create Pyraminx patterns on the Mastermorphix. For example, this is a fairly accurate imitation of the Pyraminx's Tri-color Clover.

This pattern can also be created on the Magic Octahedron and Tutt's Icosaminx.

This pattern doesn't exploit the shape-changing capabilities of the Mastermorphix, but I'm working my way up to that!

Pyraminx Tri-color Clover

There are really four colors on each side, a "background" color and three differently colored flower petals. Yeah, it's abstract.

This is closely related to the colors you'd get if you started with a solved Pyraminx and just rotated each of the tips clockwise by 1 turn. But it's a nice prelude to my next post.

5x5 Interlaced Spirals

My goal was to create a spiral path from the center to the outer edges. There's not more much to say about this one!

5x5 Dodecahelix

In this pattern, a string visits each face twice as it winds its way around the cube. The two green/yellow faces are turned a quarter turn from each other.
Since it's not entirely clear from the photo above, I've included a schematic diagram at right.

This is another of those patterns that's most interesting in person because you can follow the string around the cube. Or you can try, anyway. It's easy to lose count before following it around all twelve faces in the pattern!

Octahedron Four Clovers

My previous Gnostic Triquetra attempted to demonstrate how the Magic Octahedron could be divided into odd-and-even faces with two different patterns. This pattern shows it a bit more clearly: four sides have clovers, and four sides are blank.

The pattern is arranged so each face with a clover is flanked by three adjacent blank faces. And each blank face is flanked by three clovers.

4x4 Tricolor Python

This pattern is related to the 5x5 Quad-color Python pattern I posted a few months ago. It retains the off-center stripes, which were the most challenging part of the 5x5 pattern.

5x5 Flipped DNA

This pattern is a another double-helix like the previous Twisted DNA with a somewhat ore complicated color scheme. In this instance, the colors on each face are flipped onto each adjacent face. For example, the white face shown above has a green stripe and the adjacent green face has a white stripe. The white face also contains a red stripe, and the adjacent red face also contains a white stripe.

This color scheme extends around the entire cube, as shown at right.

Because the colors are flipped from adjacent faces, all six colors are visible when the cube is viewed diagonally. At left the trio of red-green-blue faces contain stripes in white-orange-yellow. Naturally the white-orange-yellow faces must contain red-green-blue stripes.

I used different color groupings from the previous Twisted DNA (which was white-green-orange and red-yellow-blue) because
it provided better color-contrast for this pattern.


Both patterns are best when viewed firsthand because you can trace the double-helix all the way around the cube...

5x5 Twisted DNA

A pair of threads twist over and under each other, wrapping around all six sides. Shown at right, the color scheme is based on two ordinary 3-cycle twists. It's essentially two snake type patterns woven together to depict a DNA-like double-helix.

Because the color scheme is based on a 3-cycle rotation, the cube shows three colors on three sides when viewed diagonally as shown in the picture at left.

4x4 Water and Fire

I named this simple 4x4x4 pattern for the 3-color groupings into cool and warm colors representing water & fire. I stumbled onto this pattern while playing with a big, cheap 4x4x4. It works pretty well, despite the cheap price.

5x5 Dots Cube in Checkerboard Cube

This is a variant of the common Cube In Cube pattern in which the inner cube and outer cube are also depicting common patterns Dots and Checkerboard.

I tried to invert it into a Checkerboard Cube in Dots Cube,
as shown in the smaller picture at right. I don't think it worked as well, but it's still visually interesting . . . and an entertaining challenge to construct.

"Awful" Waffle

This just didn't work.

I worked out how to arrange the colors in a sort of "Waffle Weave" arrangement, but when I tried it out on a 4x4x4 cube it looked horrible. Really, just look at it!

So I tried again on a 5x5x5, hoping the background color between the stripes might make them more visible. It did, but it still looked awful.

Oh well, I've got better ideas...

[Edit] Patrick C noticed the Waffle pattern is somewhat clearer if you concentrate on just one face at a time. Sure enough! From the angle shown below, the pattern is even visible on the 4x4x4. (If you squint.)

5x5 Cube in Cube in Cube in Cube in Cube

Cube pattern expert Per accurately pointed out that my 4x4 Quad-color Boxes pattern is basically a mixture of two common patterns. I decided to push the concept to its maximum extreme, which you can interpret as five nested cubes or five nested rings.

Octahedron Black Widow Spider

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.

Octahedron Gnostic Triquetra

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.

Octahedron Gale Warning

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...

Pryaminx Gale Warning

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.)

5x5 Quad-color Snake

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.

Orthogonal Pinstripes

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.

Triskelion

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:

5x5 Spring Time

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.