4x4 Quad Color Python

Four colors per side on a 4x4!

This pattern surprised me. My 5x5 Quad Color Python demonstrated 4 is the maximum number of colors per side for a 'python' type pattern on a 5x5 cube due to combinitoric constraints imposed on the centers and middle-edge pieces. I later reproduced the pattern on a 4x4 by just eliminating the center string, yielding the 4x4 Tricolor Python pattern.

While exploring how the pattern might be extended onto a 6x6 cube I realized I had overlooked a better implementation of the pattern on the 4x4. Instead of eliminating the center stripe I moved it and replaced one of the edge stripes. The picture at right compares the 4x4 and 5x5 versions of the improved 'python' pattern, showing that the sides of each cube have the same four colors although they appear in a different order.

5x5 Grecian Urn 2

This string pattern has the same layout as my previous Grecian Urn 1 but with a somewhat more complicated arrangement of colors, so the side faces have four colors each. No two string fragments on the same face are the same color.

Too complicated? Here's a schematic showing how the pieces are laid out on the cube.

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.

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...

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.

5x5 Quad-color Python

The term "Python" usually describes a rope pattern that winds around the entire cube in a repeating pattern of turn-right, turn-left, straight.

It was surprisingly difficult to devise a workable color scheme because the off-center Pythons have two different sets of constraints, one for the face cubies and another for the edge cubies.

Other than the obvious substitution of different faces (ie: reflections or rotations) I could identify only two schemes. The two cubes below show how the two schemes have the same colors on each face, just in a different order:

4x4 Quad Color Boxes

At first this looks like a rotation around a single corner, but the cubie placement is a little more complex to allow four colors per side. An ordinary rotation pattern has no more than three colors per side.

Another distinguishing characteristic is that all six face colors are visible from each of the two views.

This is a Meffert's Master Cube from the mid-1990's when they were using tiles in a color scheme with red opposite white.