Lights Out 4D
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mananself
Mar 1, 2026, 1:57:56 AM (9 days ago) Mar 1
to hypercubing
Hello everyone,
I made Lights Out 4D: the classic puzzle game, but on stereographic projections of 4D polytopes.
https://www.nan.ma/lights_out_4d/
It's a webpage that works on phone, tablet, or desktop. You can change viewpoints in 3D (swipe on touch screens or drag with mouse) and 4D (pinch on touch screens or scroll with mouse wheel). Use the "+"/"-" buttons to zoom in/out.
There are three basic polytopes to choose from: 16-cell, 24-cell, and 600-cell. For these polytopes, edges form great circles (rings). You click a vertex to toggle the state of the rings passing through it. The objective is to turn off all rings.
After the initial launch, I added two lesser-known shapes: bicont and bideca. They are the duals of the bitruncated 24-cell and bitruncated 5-cell, respectively.
== Why I made this puzzle ==
Lights Out puzzles are much easier than twisty puzzles because the moves are commutative. That also means you can play with 4D shapes more casually, on a touch screen. This has been one of my long-term goals.
The motivation for Lights Out 4D came from the Mirror_Z puzzles in MPUlt: 3^4, 24-cell, 120-cell, and 48-cell. In these puzzles, there's only one operation per cell: center-inverting it. The 2C pieces move in many orbits, each of which is a great circle. The parity analysis of these orbits is an interesting sub-puzzle that works just like Lights Out: inverting a cell changes the parity of all the great circles passing through it. Fixing the parity of all orbits is a necessary step toward solving all the 2C pieces. When I solved these puzzles, I found this step particularly interesting, especially for the 120-cell and 48-cell Mirror_Z. However, not many people have had the chance to appreciate it, because few have attempted the full puzzles. So for a long time, I've wanted to extract this step into a standalone puzzle that more people could play on more platforms. Lights Out 4D is that idea realized.
The 3C pieces of the Mirror_Z puzzles are also interesting. Each orbit is an S^2 sphere: an equatorial sphere of the 4D polytope. The parity analysis is even harder for the 120-cell. It's also a Lights Out puzzle. Under stereographic projection, these orbits look like intersecting bubbles. Since turning bubbles on and off would block the view behind them, I don't have a good way to visualize it in this version, so I'm only implementing the 2C part here.
== Why I made this puzzle just now ==
The idea of Lights Out 4D had been sitting in the back of my mind for over 10 years, because I was never motivated enough to build it. Recently, coding AI has progressed to the point where I decided to give it a try. After about an hour of chatting, it produced a playable first version. I spent two more days debugging, expanding, and polishing it into what it is today. I'm probably capable of creating it without AI, but I definitely wouldn't have been able to produce a fairly refined game in just two days. In short, thanks to AI, we're playing this game now.
Try it out and share your thoughts! Thanks!
Nan
I made Lights Out 4D: the classic puzzle game, but on stereographic projections of 4D polytopes.
https://www.nan.ma/lights_out_4d/
It's a webpage that works on phone, tablet, or desktop. You can change viewpoints in 3D (swipe on touch screens or drag with mouse) and 4D (pinch on touch screens or scroll with mouse wheel). Use the "+"/"-" buttons to zoom in/out.
There are three basic polytopes to choose from: 16-cell, 24-cell, and 600-cell. For these polytopes, edges form great circles (rings). You click a vertex to toggle the state of the rings passing through it. The objective is to turn off all rings.
After the initial launch, I added two lesser-known shapes: bicont and bideca. They are the duals of the bitruncated 24-cell and bitruncated 5-cell, respectively.
== Why I made this puzzle ==
Lights Out puzzles are much easier than twisty puzzles because the moves are commutative. That also means you can play with 4D shapes more casually, on a touch screen. This has been one of my long-term goals.
The motivation for Lights Out 4D came from the Mirror_Z puzzles in MPUlt: 3^4, 24-cell, 120-cell, and 48-cell. In these puzzles, there's only one operation per cell: center-inverting it. The 2C pieces move in many orbits, each of which is a great circle. The parity analysis of these orbits is an interesting sub-puzzle that works just like Lights Out: inverting a cell changes the parity of all the great circles passing through it. Fixing the parity of all orbits is a necessary step toward solving all the 2C pieces. When I solved these puzzles, I found this step particularly interesting, especially for the 120-cell and 48-cell Mirror_Z. However, not many people have had the chance to appreciate it, because few have attempted the full puzzles. So for a long time, I've wanted to extract this step into a standalone puzzle that more people could play on more platforms. Lights Out 4D is that idea realized.
The 3C pieces of the Mirror_Z puzzles are also interesting. Each orbit is an S^2 sphere: an equatorial sphere of the 4D polytope. The parity analysis is even harder for the 120-cell. It's also a Lights Out puzzle. Under stereographic projection, these orbits look like intersecting bubbles. Since turning bubbles on and off would block the view behind them, I don't have a good way to visualize it in this version, so I'm only implementing the 2C part here.
== Why I made this puzzle just now ==
The idea of Lights Out 4D had been sitting in the back of my mind for over 10 years, because I was never motivated enough to build it. Recently, coding AI has progressed to the point where I decided to give it a try. After about an hour of chatting, it produced a playable first version. I spent two more days debugging, expanding, and polishing it into what it is today. I'm probably capable of creating it without AI, but I definitely wouldn't have been able to produce a fairly refined game in just two days. In short, thanks to AI, we're playing this game now.
Try it out and share your thoughts! Thanks!
Nan
Marc Ringuette
Mar 1, 2026, 11:36:43 AM (8 days ago) Mar 1
to hyper...@googlegroups.com
Hi,
Nan,
The simplicity, naturalness, and usability are great, and it's quite pretty! Platform agnostic, too. Thanks for making it, I call it a big win.
These lights-out puzzles are also easy enough to be a pretty good entry into 4D puzzles for folks, I'd imagine. Simple hill climbing gets you pretty far, and the remaining lights-on circles pop out nicely in their bright colors, providing a natural simplifying/focusing mechanism toward the end.
For the 600-cell, I had no idea if it was going to be too hard or what. In the end, I managed to pan and zoom and 4d-zoom around to finish it in 170 moves, maybe half an hour. Toward the end I concocted a zooming-around strategy where I'd make pairs or triplets of the more lit-up cells visible at the same time, then try toggling them in combinations looking for improvements. Major retreats or retrenchments didn't seem to be necessary, nor a real understanding of the puzzle space, which is just as well, because I didn't have one. I was just making colors pop out of the spaghetti and poking at them until I made increments of progress.
You rock!
Marc
The simplicity, naturalness, and usability are great, and it's quite pretty! Platform agnostic, too. Thanks for making it, I call it a big win.
These lights-out puzzles are also easy enough to be a pretty good entry into 4D puzzles for folks, I'd imagine. Simple hill climbing gets you pretty far, and the remaining lights-on circles pop out nicely in their bright colors, providing a natural simplifying/focusing mechanism toward the end.
For the 600-cell, I had no idea if it was going to be too hard or what. In the end, I managed to pan and zoom and 4d-zoom around to finish it in 170 moves, maybe half an hour. Toward the end I concocted a zooming-around strategy where I'd make pairs or triplets of the more lit-up cells visible at the same time, then try toggling them in combinations looking for improvements. Major retreats or retrenchments didn't seem to be necessary, nor a real understanding of the puzzle space, which is just as well, because I didn't have one. I was just making colors pop out of the spaghetti and poking at them until I made increments of progress.
You rock!
Marc
mananself
Mar 1, 2026, 11:43:54 PM (8 days ago) Mar 1
to hypercubing
Hi Marc,
Thank you for playing. I'm really glad you enjoyed it.
About solving strategy, I'm also using the greedy algorithm to click the vertices with a high number of lit-up rings. For the 600-cell, usually this strategy works. Occasionally, I'm stuck in a local minimum where all the vertices have two lit up rings, then I didn't know the next move other than clicking an arbitrary intersection.
For the fourth shape, bicont, somehow it's easier to run into local minimum with only two colors left, and all relevant vertices having two lit-up rings. I don't have a strategy yet, but that probably requires a real algorithm to tackle.
Nan
M Nastri
Mar 4, 2026, 12:41:42 PM (5 days ago) Mar 4
to mananself, hypercubing
Nan,
You are absolutely right. This puzzle is awesome and I'd never found out about it if you hadn't developed it. So thank you for that.
I'm really impressed by how well this works on mobile. It has such a good feel and responsiveness. Great job!
Also AI assistants FTW =).
Thanks for sharing, now let me tackle this 600-cell monster.
Best regards,
Nastri
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Suqin Tan
Mar 4, 2026, 6:55:04 PM (5 days ago) Mar 4
to mananself, hypercubing
Hi Nan,
This is such an awesome game! My 11-year-old son loved this game the moment he saw it. This game is now his favorite. He gets it fast with 16-cell and 24-cell. I think he is struggling with the 600-cell. I am going to share these discussions with him for some inspiration.
Cheers,
Suqin
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