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What is hypercubing?

Hypercubing is the hobby of solving twisty puzzles (like the Rubik’s cube) in higher dimensions and exotic geometries.

Isn’t the 4th dimension time?

While time is one dimension in 4D spacetime, it behaves completely differently from the three spatial dimensions. Hypercubing deals with higher dimensions of space, where all dimensions are interchangeable.

How can we visualize 4D?

Our eyes see only a 2D projection of the 3D world, and we’re able to reconstruct the 3D world around us with only minimal difficulty. Using mathematics, we can project a 4D shape onto 3D, and then project that 3D shape onto 2D to be displayed on a computer screen. With enough practice, it’s possible to reason intuitively about higher-dimensional space using these visualizations.

Where can I interact with other hypercubers?

Before the Google Group or Discord server, there was a Yahoo Groups mailing list. Those messages are archived here.

Virtual puzzles

What program should I download?

For getting started, we recommend Hyperspeedcube. See the software page for a list of hypercubing software and feature comparisons.

How do I learn to solve the 3x3x3x3?

We highly recommend that you figure out how to solve the 34 on your own. It’s a fantastic puzzle and you’ll learn a lot!

  1. Learn how to solve a 3x3x3, ideally intuitively. There are plenty of tutorials online, although you should try it on your own first. It’s a good challenge!
  2. Download Hyperspeedcube or use the web version.
  3. Follow this video to get aquainted with the program:

Once you feel comfortable solving 33 from a full scramble and 34 from a 1-move scramble, you know everything you need to do a full solve. If you get stuck, you can ask for help on the Hypercubers Discord server.

What methods exist for the 3x3x3x3?

Many 3D methods can just be scaled up and used on the 4D cube. Some notable methods are:

As of 2024, 3-Block is the most popular speedsolving method and what’s used in the world record, but CFOP is also competitive.

How do I start learning to solve 4D puzzles?

First, download Hyperspeedcube or MC4D and start experimenting with the 34! Try to solve one-move scrambles and keep practicing that until you’re comfortable. Once you can solve one-move scrambles with ease, pick a method to learn.

Why not start with the physical 2x2x2x2?

You will never understand physical puzzles before understanding virtual puzzles. Computer simulations are the most direct way to experience 4D puzzles, and it’s what all physical puzzles are emulating. It’s effectively impossible to develop new physical puzzles without first understanding the equivalent virtual puzzles.

Grant Staten

I think that approaching hypercubing by starting with only physical puzzles does not lead to an understanding of how the puzzles actually work. Even if you can solve them.

Before I touched a virtual puzzle, I had:

  • almost gotten sub-2 on a physical 24 I’d built
  • started building physical 2x2x2x3
  • rendered physical 2x2x2x3, 2x2x3x3, 2x3x3x3 (piggybacking off of Luna’s work and just following patterns in place)

However, looking back, I 100% honestly did not yet understand how any of those puzzles actually worked at the time.

I have absolutely nothing against someone only focusing on physical puzzles. But in my experience you don’t gain an actual understanding of how the puzzles work through solely using the physical puzzles.

Why not start with the virtual 2x2x2x2?

The 24 is particularly disorienting for beginners because half of the puzzle turns at once. As a result, while the 24 strategy is technically simpler, it’s actually more challenging to wrap your head around, especially when you’re new to 4D puzzles. Just like how the 33 is a better starting puzzle in 3D, you can learn lots of important concepts from the 34 that will help you with other 4D puzzles.

Sergej Volkov

I regret not starting with a 34. I first solved virtual 24 using Rowan’s physical method and it was extremely painful and did not really help to develop any 4D intuition. I ended up just drawing the physical representation of the puzzle on a piece of paper.

What is God’s number for [puzzle]?

See God’s Number.

Physical puzzles

What is a physical 4D puzzle?

The physical 4D puzzles are puzzles that are perfectly analogous to the virtual 4D puzzles, but implemented in the physical world. See these links:

How can I buy a physical 2x2x2x2?

See the Ordering Melinda’s 2x2x2x2 on the Superliminal website. Also see Melinda’s 2x2x2x2 on the Superliminal site, which includes the history, statistics, and Hall of Fame.

How can I buy other physical puzzles?

Melinda’s 24 is the only physical puzzle for sale. The physical 34 and hypercuboids are currently one-of-a-kind. If you want one, you need to design and 3D print it yourself.

Can I download 3D files for the physical 2x2x2x2?

No. Melinda has put a lot of work into her physical 24 designs, and invested quite a bit of her own capital into selling prototypes at a loss and getting them mass-produced, so we respect her wishes to not make those files public. If you want to create your own files modeling Melinda’s physical 24 and 3D print them, that is fine, but we ask that you do not make the files avaliable for download unless Melinda is OK with it.

What physical 4D puzzles have been built?

See Physical Puzzles for a comprehensive list.

What physical 4D puzzles are possible?

While it’s always possible to just arrange the stickers on a table, the real challenge is in finding a design that is piece-based instead of sticker-based and fits in a compact shape that isn’t too horrendous to turn. This requires some out-of-the-box thinking and, in extreme cases, application of group theory. We currently have several renderings for physical puzzles that haven’t been built in real life yet; see the Physical Puzzles page for an incomplete list.

Hyperspeedcube

Does Hyperspeedcube run on my OS?

Hyperspeedcube runs natively on Windows, macOS, and Linux. There is also a web version, which runs on Chromebooks or other devices where the downloaded version does not work. For mobile phones, it is possible to run Hyperspeedcube in a browser but not recommended. See Software for alternatives.

I get an error when I try to run Hyperspeedcube

See Hyperspeedcube - Troubleshooting.

How do I use keybinds in Hyperspeedcube?

How do I use piece filters in Hyperspeedcube?

Hyperspeedcube 2

When will Hyperspeedcube 2 be ready?

When it’s done. Hopefully before summer 2025.

What features are planned for Hyperspeedcube 2?

See Hactar’s website.

Does Hyperspeedcube 2 have [feature] yet?

See Hactar’s website.

Can I download the latest development build?

You can access the latest development builds either by donating to Hactar on Ko-fi (any amount one time should work) or building it yourself from the source code, which takes some time to set up but generally isn’t too hard.

I’m having troubling with Hyperspeedcube 2?

Please do not ask Hactar for help building or using development builds of Hyperspeedcube 2 unless the build on Ko-fi is broken. Everything in the program is subject to change, and any time spent helping an individual user is time that could instead be spent writing documentation.

Where can I follow the latest development updates?

See the Hyperspeedcube 2.0 Development Updates thread in #hyper-forum on the Hypercubers Discord Server. Once Hyperspeedcube 2.0 is ready for general use, there will be an announcement that pings the @Hyperspeedcube Update role (and possibly @everyone).

Speedsolving

What are the speedsolving records for 4D puzzles?

See the leaderboards. To get on the leaderboard, read the submission guidelines and submit a video of your solve to this form.

Why not use speedrun.com?

Speedrun.com does not allow “generic Rubik’s Cube simulators.” We applied and were rejected.

I don’t know full OLL/PLL/ZBLL/etc. Can I still get fast at 4D?

Absolutely! Most 4D speed methods are highly intuitive, and world-record times often use just 2-look OLL and PLL. Executing algorithms is a very negligible part of the solve compared to the massive amounts of pair or block building.

Hactar (mid-2024)

Ok I actually ran the numbers:

Consider that the second solve is basically the best case for a 2-look last layer (the goal of full OLL+PLL), using algorithms that have really nice RKT cancels and are easy to execute with my keybinds and I’ve practiced them a ton, but it was still only 4 seconds faster, which is ~2% of the total solve. Additionally, my experience is that it takes much more practice to execute 4D algorithms at max speed with a keyboard compared to executing 3D algorithms at max speed on a 3^3.

Based on all that, I can confidently say I don’t think full OLL+PLL will ever be meaningfully better than RKT-canceled 2-look OLL + 2-look PLL, with one exception: There’s a handful of full OLL algorithms (namely the ones composed of fruruf and sune) that I think are worth using if you know them from 3D, but aren’t at all crucial. I do use these during 4D solves when I recognize them, and with some effort we may be able to find a few more cases with easy cancels, but I don’t think it’s worth learning these just for 4D solves.

What 4D algorithms are there?

There’s so many cases for each step of the solve that creating a complete algorithm set is basically impossible, and there’s so many options for moves that algorithm explorers are infeasible. Almost every algorithm we have is based on an algorithm from 3D, and the only search program we have is a sort of optimizer for one very specific kind of algorithm derived from 3D.

How can I get faster at solving 3x3x3x3?

First, learn 3-Block! Pairs are more popular since the recognition is easier, but solutions using triplets tend to be shorter; as far as we know, both are viable. If you’re getting times in the 8-15 minute range, do slowsolves where you focus on efficient solutions to F2L pairs/triplets.

Hactar

From most to least significant:

  • 1-key-per-move keybinds that prioritize R and I cells. This is more than 2x faster than default keybinds, because you do not need to time the release of keys.
  • 1-key-per-move RKTbinds with RKT cancels. These two optimizations complement each other so well, because it spreads out the work among all your fingers.
  • Single keys for some 180-degree turns, because repeated keys are slow! By adding keys for x2 and y2, you can reorient a cell into any orientation with just two keypresses.
  • RKT-canceled triggers during F2L-3. I leave debt on U and have muscle memory for the common RKT-canceled trigger R (flip) U' R' (flip) (where (flip) = {1-2}Ozx2), its inverse (flip) R U (flip) R'*, and their back and left-handed forms. This + U moves accounts for basically everything you do in F2L other than R U2 R', which you can usually avoid or in worst case just (flip) R (flip) U2 (flip) R' (flip).

How could the 3x3x3x3 record be improved?

Hactar (mid-2024)

Here’s what I think would make a big difference, from most to least significant:

  • Lookahead during F2L-4. This is essentially unexplored.
  • Optimal solutions for F2L-b cases. My gut says this could save an average of ~3 moves per pair over my solutions during left block, and ~5 moves per pair during right block, which adds up to ~30 STM saved. I think there’d be some value in a comprehensive study of 3-block F2L cases and what techniques are effective in solving them, and research into the psychology of how to recognize them. For some examples of what I mean: I remember reading somewhere that on 3^3 it’s better to find an F2L corner and then search for the matching edge, rather than the other way around. I also know that once you find the edge, you can recognize its orientation to know whether you can solve the pair using just or whether you need less-ergonomic moves. Figuring out and documenting these sort of tricks for 4D would help.

I think both of those improvements could save 15-30 seconds, bringing it from ~1:15 to ~0:45. I also feel like general lookahead/efficiency improvements in PLC might save 10-15 seconds but I can’t put my finger on exactly what they would be. I know my OLC feels very variable during solves, but in practice I can brute-force pretty much anything into a valid final case by spending a second or two flipping one edge/corner.

Does this puzzle exist?

2D Rubik’s Cube

Depending on how you define “2D Rubik’s cube,” it might or might not exist.

A 3D Rubik’s cube has 6 square faces and each face twists within its 2D plane (with 4 possible rotations). A 4D Rubik’s cube has 8 cubic cells and each cell twists within its 3D plane (with 24 possible rotations). By analogy, a 2D Rubik’s cube has 4 edges and each edge can be rotated within its 1D line … but there’s no way to do a rotation in 1D. So if twists have to be rotations, then a 2D Rubik’s cube doesn’t have any turns and so isn’t a puzzle (or is a trivial one).

Using different definitions, we can create a few different puzzles that could reasonably be called a 2D Rubik’s cube:

  • If we allow reflections instead of rotations, we get the Reflesquare, which generalizes to the Reflecube.
  • If we allow translations instead of rotations, we get Loopover.
  • If we allow circular cuts instead of flat cuts, we get various MagicTile puzzles, including some that are actually equivalent to an ordinary 3D Rubik’s cube!

4D Square-1

Square-1 is fundamentally a bandaged dodecagonal prism. There are so many ways to extend that into 4D that there isn’t really a canonical “4D square-1”

4D Skewb

There’s so many ways to generalize a skewb to 4D that we have a whole page full of them!

8-dimensional and higher

Above 5 dimensions, cube puzzles aren’t more difficult or interesting, just more tedious and computationally expensive. But there might be some wild hyperpuzzles yet to be discovered up there, say one based on the very special geometry of the E8 Lattice!

3D Rubik’s Clock

Instead of rotating circles in 2D, you can rotate spheres in 3D. This is a more interesting puzzle than the traditional Rubik’s Clock because moves don’t commute. No one’s written a program yet to simulate it but you totally could!

How do I make a 4D [thing]?

✨ Generalising Things to 4D: A Handy Guide ✨

  1. Understand and define the thing you’re generalising
  2. Find where your definitions reference or assume something dimension-specific
  3. Rewrite your definitions to avoid dimension-specific references or assumptions
  4. Find what 4D object fits your new definitions (there may be one, several, or none)