Pentominoes get WEIRD in 3D Space!

Sorry for the odd audio quality! I moved around a lot this month and I ended up re-writing and re-recording the script several times, so different parts of the script were recorded in different rooms. Not the best habit... but there just ended up being so much interesting torus stuff to talk about, so how could I not!

First Pentomino Facts Video:

Pentomino Pathfinding video:

Spreadsheet for tracking every 5x5 pathfinding on a torus solution:

MUSIC USED (In order)
Patricia Taxxon - Astral 2
Kevin Macleod - Raving Energy
Platinumquest Soundtrack - Tranquility
Stevia Sphere - Floating on the Water

[mateuszszulecki]

8:08 What's funny about that name is that John Conway's proposed naming scheme for pentominoes actually *did* use O for the straight shape, as well as Q for the L, R for F and S for N.

[MemeAnt]

4:17 just take the solution us speedcubers took. Call it a G. (For anyone wondering, there are 4 wacky algorithms which are all called “g-perm, ” and they move around a truly unholy number of pieces and don’t look like much of anything)

[arturbueno]

When I tell you I RAN to get my earphones as soon as I saw this video pop up, I love this series sm

[diegonals]

I've been seeing this myself, and in a 3x3 torus, the T, X, and L pentomioes are the same, as well as the P and U ones. This means the only 'unique' pentominoes are I, N and W, or WIN

[Negreb]

You know it's a good night when deckard posts a video

[nerdiconium]

5:20 I’m personally torn between 38 and 63. If one declares that a pentomino is defined only by what squares compose it, then the Q pentomino is truly its own thing that arises due to the torus shape. On the other hand, if you hold that the pentominoes must inherit a “normal” boundary from the flat pentominoes, then all possibilities (that don’t repeat pentominoes) must be considered, including any that can’t be made equivalent to previous by picking up and translating/rotating the torus. 47 seems like the hardest to justify, though I realized that certain pencil puzzles about pentominoes may like that number, where it is just a set of squares but the identity of the pentomino is still important (“Let’s get cracking!”)

[Codex]

"Take the 63 solutions" then you would be saying that rotating the X pentomino is a different solution, quadrupling the number of solutions by FOUR (that contain the X pentomino obviously)

[shirinpatel]

5:38 amputated W
Also, 4D Pentominos:
1. Each pentomino has a [RECTANGULAR] border
You may shift pentominos 1 space across the grid like a torus. This means an pentomino L can go backwards and a hexomino L can turn into a and backwards as well
Hypercube boards are complicated so I’ll explain simply
2. They are like cube boards but every layer inward pentominos shift a space (any direction)-wards. Paths are allowed to go between layers.
A 4*5*6*2 board is a 4*5*6 board with an extra layer inside. Every layer is like a board of its own. Rukes do not apply to different layers (i.e. you are allowed to use the same -mino twice in a hypercube board)
3. Also, you represent 4D pentominos/boards by making deeper layered pentominos smaller. Pentominos can be in different layers at the same time. Shown at rule 4
4. And since names will run out at some point, you will have to use a harder-to-understand notation.
Anything that is not 0 is a mino. 0s are empty. Higher numbers is a deeper layer, so 2 is 1 layer deeper than the surface. Here is an example of a Q pentomino v.[Pentominos are allowed to have diagonals.]
11
11
2
This may all sound really complicated but I will show pictorial representations on another website. Link below

[jakobr_]

63 makes the most sense to me. It’s the number of ways to carve up the occupied cells into the shapes that we’re playing with. Different reflections and translations of the two weird ones are carved up in different places.

[linguini]

Honestly pentominoes in 2d hyperbolic space would go hard

[potaatobaked]

I personally would go with 38 solutions for the 4x4 torus. Mainly because I work with weird geometries a lot, and I consider the pentominoes to be fundamental to the geometry they are in, rather than universal (just for many there are obvious maps to the flat case). On the topic of weird geometries, while I'm sure it would be a nightmare to figure out, I'd be interested to see pentominoes on hyperbolic square tilings.

[a-cdlw]

I'd call the pentomino at 4:15 the "Ω" Pentomino. Also a 4 torus wraps around no matter what, so i choose 63 solutions.

[atavoidirc]

4:18 R pentomino is taken, used by the CGOL community as their name for the F pentomino.

[orrinpants]

I found this in my recommendations soon after it was posted. I feel lucky, but really I think the algorithm knows I was waiting for this videos release and would've suggested it whenever it was uploaded

[kylewood]

5:17 I say 88. Q Pentomino is a distinct shape that isn’t L or Y.

When you draw borders around the shapes, you can see the way they are used. That is distinct in my book

[navidryanrouf]

Is this a part 1, part 2, part 3, part 3.5, part 3-1, part iii, part 11 (in binary), part ٣, part ৩, part 三, part 弎, part 叄, part ३, part ፫, part γ, or perhaps something else? 🤨
(Idk I got tired continuing the joke and gave up after realising I needed to do it for ones and twos)

[geothermie_]

63 that's the most coherent solution :
The idea of a pentomino existing only on certains grids break the basic principle of categorisation.
Not considering different orientation of a pentomino but considering same shapes formed by différents pentomino as différent solution isn't coherent.

[seanthefurcorn]

5:37 I feel like calling it a chair because it kind of looks like one.

[beagle_uah]

Great work again, Deckard! Can’t wait to see Cubonimos lol

[AppIePineapple]

I literally JUST watched the more pathfinding video