That the knowledge at which geometry aims is knowledge of the eternal.
-- Plato

As the beginning of Part III: Crafting Hyperskewb, I have to explain what is skewb first. For those who are here to see what a hyperskewb is, sorry, not today. Let's recall 3D skewb (a normal skewb).

skewb

Some online resources first:

• grubiks: introduction, projection, playable (but the control is not satisfying).
• ruwix: introduction, net, playable (button-based control is good, but the net representation can be confusing to those who never saw the puzzle before).
• Z3cubing's tutorial: I don't watch tutorials, so I am not really sure how good this skewb tutorial that ranks the highest in the youtube search is. At least, you can see how a skewb is played.
• Wikipedia: Skewb

Notations

As suggested on the ruwix page, we will follow the L/F/R/B notation. They all refer to bottom corners. For your reference, the left-bottom corner in ruwix's net presetation, corresponds to Left; the right-bottom corresponds to Front, and so on.

Mechanism & Geometry

The whole puzzle is a cube, but the axes for rotation is quite different from a 2x2x2 (pocket cube below), and thus it has different cuts and appearance. If I can only give you two keywords about the mechanism of a skewb, I would say corner turning and deep cut.

Corner turning, contrary to face turning like pocket and Rubik's cube, you twist the puzzle around the corner. In other words, the rotation axis of any group of the parts is no longer perpendicular to any face, but is a ray from the center point (a.k.a origin) of the cube to the vertex of the corner.

Compared to a normal cube, the symmetry of a skewb also differs. A quarter turn to a normal cube is 90 degrees, so each 4 turns on a face keeps the state of the cube unchanged. To a skewb, a turn is 120 degrees, so the cycle is of length 3.

A deep-cut puzzle is a puzzle that there are cutting surfices divides the puzzle into two isomorphic groups. Both 2x2x2 and skewb are pure deep-cut puzzles, because all their cuts go through the origin. This attribute cannot be emphasize more for a precise hyperskewb definition. An old discussion in the hypercubing archive states that a 4D skewb is not deep cut. We will come back to this thread later in Part III, but I don't agree with that.

Note that the cut surface of skewb is a regular hexagon. While a regular hexagon has six rotation symmetries, only three among them can remain a skewb in a cube shape.

Conclusion

The reader should know what is a skewb now. Let's play with it tomorrow.

小結

介紹 skewb 的基本術語、結構與幾何特性。