On an old thread about 4D skewb

[Quey-Liang Kao]

Hi hypercubers,

I found this thread (https://superliminal.com/cube/pages/393.html) in the archive, in which Matt Galla has claimed the "4D skewb" name. I would like to know, was there any progress on the realization of the 4D skewb proposed by Matt?

I'm interested in this because, I'm doing a project named hyperskewb, in which I try to generalize the concept of skewb in higher dimensions since 4D. It is sill a work in progress, but I expect it will be playable by the end of September. It will be just a WebGL page (with quick-and-dirty JS) so you can host a simple local http server and try it then.

Thanks,

QL

[Roice Nelson]

Hi QL,

Yes, Andrey's Magic Puzzle Ultimate is very generic and can support a 4D Skewb. It looks like it is not included by default in the 4D->CubeBased puzzles section, but... you can extend the entries in the MPUlt_puzzles.txt configuration file. A way to get started with that is to copy existing puzzles and edit the "Cuts" or other properties. Here was a quick effort that might be considered a 4D Skewb.

Puzzle 4D_half_skewb
Dim 4
NAxis 1
Faces 1,0,0,0
Group 1,0,0,0/1,1,0,0 1,0,0,0/1,0,1,0 1,0,0,0/1,0,0,1
Axis 1,1,1,1
Twists 1,1,-2,0/2,-1,-1,0 1,1,-1,-1/1,-1,-1,1
Cuts .25 -.25

Playing with this, it seems the Skewb can arguably be generalized in different ways. These cuts make the hypercube faces look like Skewbs, but I'm not sure that is the essence of skewbiness. Maybe Andrey's "4D_half" puzzle has the soul of a Skewb, since it is deepcut and slices cut the hypercube in half (?)

The above is likely not exactly "right" btw - I haven't looked at the other properties closely, nor studied the difference between his 4D_half and 4D_half(alt) versions. But hopefully, this is enough info for you to experiment.

And in any case, a WebGL page would be a cool addition!

Best,

Roice

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[Quey-Liang Kao]

Hi Roice,

Thanks to the quick feedback and the reference to MPUlt.  It was on my survey list and I tried it on my linux box with some .Net workaround, but still couldn't get a proper display, so unfortunately I won't be able to dive into the software anytime soon.

Regarding skewbiness, you had a similar perspective in the archived thread, 

> my personal preference leans towards not using terms
like "4D Skewb", unless all could agree on the most defining Skewb-like
properties. Since a 3D Skewb is a vertex-turning puzzle with slices halfway
between diametrically opposed vertices, it could be argued that the 4D Skewb
must have all these properties, with the only change being that the
properties are now applied to a hypercube (in other words, that the 4D Skewb
is the puzzle you described that has faces that look like Dino cubes).

My re-implementation of hyperskewb will be like what you mentioned instead of Matt's. So yes, every cell of it looks like a dino cube. 

As a reference visualization, the following clip shows 1 cell piece (red octahedron), the 8 other cell pieces (yellow regular tetrahedron) and 12 edge pieces (blue tetrahedron).  Sorry for the large explode distance, so it does not look like a dino cube at the first glance.

> And in any case, a WebGL page would be a cool addition!

I will update this thread when it is ready :)

Thanks!

QL

[Quey-Liang Kao]

Oh, after some more survey on MPUlt, I believe my idea will be a re-implementation to Its Half-cut tesseract: https://superliminal.com/andrey/mpu/pic4.jpg

 

Quey-Liang Kao 在 2022年9月10日 星期六下午4:41:34 [UTC+8] 的信中寫道：

[Quey-Liang Kao]

Dear hypercubers,

As mentioned a few weeks ago, I have been implementing a WebGL-based 4D skewb. The source code is ready at my github repo. (Disclaimer: Most of the code is written by https://pastleo.me/)

It is playable but you have to host a simple http server your self.  For example, on Arch Linux,  you can do

```

$ git clone https://github.com/NonerKao/webgl-ironman.git

$ cd webgl-ironman

$ darkhttpd ./

```

and then visit http://0.0.0.0:8080/04-lighting.html. I tried python simple http server. It works, too.

Other than this overly-simplified basic brute-force implementation, this project includes some blog post, 

- Defining hyperskewb

- 4D skewb: Basic

- 4D skewb: Twist

- Solving Level 1

- Solving Level 4

- Solving Edges

- Solving Regular Tetrahedra and Octahedra

Hope you enjoy it! All feedback will be appreciated.

For those who wonder what it is...

The host, ITHOME, is the largest Information Technology website in Taiwan, so basically most contents are in traditional Chinese. I planned to share my project with this community, so I wrote the above blog posts in English at the first place.  These posts are part of a technical blog 30-day challenge, name Ironman Contest, in which each of participant has to write one post a day consecutively for 30 days. I cover basic 4D thinking and some introduction in Part I; from learning 2x2x2x2 to algorithm discovery to the my first solve in Part II, using MC4D (what a great software!); and finally the hyperskewb (mainly 4D skewb) in Part III. Most of the Part III is provided in the above links, but implementation is skipped because my JavaScript skill is not worth mentioning at all.

So my apologize. They will be difficult to read, because I didn't follow common terms nor do I have the energy or time to refine, polish and ask a fluent person to proof reading for me.

Thanks!

QL

Quey-Liang Kao 在 2022年9月10日 星期六下午5:12:50 [UTC+8] 的信中寫道：

[Quey-Liang Kao]

I was so exhausted that I even forgot to provide the usage, especially there is no README for now...

View control is shooting-game like, that is

- W for moving towards (0, 0, z), where z is the camera's current height

- S for moving away from (0,0,z)

- A/D for moving left/right about axis Z of the graphics space. Arrow Left/Right are alias to them.

- Arrow Up/Down for adjusting the height of the camera

Puzzle control (no mouse control, no file save/load, nonconventional notations)

- explode1: The distance between stickers. As I focus on solving only edges, I set this to the minimum value so that internal stickers don't bother me.

- explode2: The distance between cells ("faces").

- X/Y/Z/X'/Y'/Z': Equivalent to mouse Ctrl+click at a boundary cell in MC4D. Pure rotation to the puzzle. No twist happens. Always reveals the originally invisible cell and pushes the cell on the "boarder" out.  This absolute coordinate is not conformed to L/R/F/B related coordinates, so the player have to know where they are looking at and which direction is which.

- reset: reset the puzzle, but not the view.

- scramble: currently level 8 only, not configurable. To hack it, change this and reload the web page (Be aware that your browser might cache the page).

- i = 0~7: indicates a clockwise twist at Octant i (following the bottom-left form from Wikipedia, in gray code). By default, the camera is at Octant 3.

- undo: undo basic moves. Basic moves are rotations and twists.

- redo (I should have just named it "do"): The accepted format is comma-splited list, in which each element can be a basic move (X'/Y'/Z' noted as non-capitalized x/y/z) or an algorithm ID. A tedious save/load can be manually done by the combination of dump history/reset/redo.

- dump history: shows the history (including scramble) in a comma-splitted list of basic moves. Algorithm ID is not preserved.

- A0~A7: the player can define any sequence here. Ai can embed Aj, and there is no protection to recursion (recursive algorithm for a twisty puzzle? I didn't protect it anyway) so be careful when copy-pasting sequences.

That's all I have. Obviously some future studies to do,

- Magic Puzzle Ultimate. Classic. It must be clever handling high-dimensional puzzle in a generic way. What are the data structures it use? Can it support God's number calculation? So many questions... Can't wait to dig into that.

- Hyperspeedcube. Looks good. I'm not a speedcubing guy, but it will be a chance to learn Rust.

- Permutation Puzzles: A Mathematical Perspective. Need to read this, for better group theory understanding.

Thanks to this community,

QL

Quey-Liang Kao 在 2022年9月30日 星期五晚上11:49:04 [UTC+8] 的信中寫道：