NOTE: Amazingly, despite there being a month of time between working on this video, the 3x3x3 and 4x4x4 pentacube pathfinding solutions were both beaten AFTER I rendered this video, but BEFORE I uploaded it. Both were beaten by a single cell, which is pretty wild.
20:00 of course it's always the X pentomino to bring it home, just like in the entire series, what a legend for somehow turning into its letter form and taking over the whole board (also hexomino facts gonna be hype once you figure out all those names)
@@thelollykitty if we're going by single character names they should be single characters on a standard keyboard. thorn isn't on most keyboards unless you're icelandic or actively use thorn for other reasons, so it would be best to just use the standard letters and numbers everyone already has access to
Actually thr series would end with pentatesseracts, as anything above that would only contain the same penta-things as before, since there's a maximum of four different directions you can take using 5 cells
@@Intergalacticprismaticcreature if you go to the spreadsheet in the description and click on the "pentomino cubes/tesseracts" link (third one from the top), that one has every 3d and 4d solution so far, along with a picture of the 3d and 4d pentominoes
This is super well done again! I hope that you'll periodically make update videos for some of the coolest new pentomino shenanigans/updated records for the existing ones, as even though I'm definitely not smart enough to figure out these on my own (haha!) I would love to see the community's continued work!
I might tbh! A lot of the stuff from all the videos are outdated now as better solutions have been found, so I think in the distant future I might do another update video once new better solutions stop being found. That would not be for a really long time though, as to give as much time as possible for people to find even better solutions for many of these boards
Actually, for the pentacube pathfinding, those split layer diagrams on the right are quite understandable for me. This is a similar to how Lonpos presents those pyramid puzzles - they have split layer diagrams too. These split layer diagrams work well for 4D too.
Here's a unifying framework for thinking of all these different varieties you have come up with (2d, 3d, torus, cube faces). I think the correct generalization is a graph G as the "space", and subgraphs with 5 vertices as the "pentominoes". The problem can then be posed as, given a connected graph G and a beginning and end vertex x and y, maximize the distance from x to y by removing a sequence of pairwise non-isomorphic k-vertex subgraphs from G. Under this definition the weird corner cases and loopy cases from the cube and torus count as distinct new pentoninos.
i've been on a bit of a bejeweled binge lately so this got me thinking of what a match 3 game would be like if it were in a cube instead of on a flat 2D plane lol
@@Iam1Person i've actually been thinking about it more and it might work better if it were in a 4x4x4 cube and you only had to match 2 gems instead of 3 lol. that'd drastically simplify it i think... i hope...
I was one of the first 10,000 viewers on this video Also, this series inspired me to make my own google sheet called "ominoes" and share it with my classmates
can't wait for some big mathematicians to discover the series and write a paper with weird symbols in which they prove and generate the paths for n-dimensional n-minos in a n-dimensional grid
FYI, spectator mode could be pretty helpful for any further visualizations where you need to travel through spaces smaller than the player. It's probably clearer to have the scaled up version so you don't phase through the walls as easily, but you could also use the scrollwheel to reduce the speed you move in spectator mode and still have a plesent experience. I'm loving the videos, though, btw!
It would be cool to see just the path that the pentacubes make in 3D. In minecraft this would mean that the air blocks become solid and the non-air blocks become transparent.
Ideas: Klein Bottle pentacube pathfinding, hypercube surface pentacube pathfinding, and hyperpentacube pathfinding! (No idea how these would be visualised though)
"I dare someone to build this structure in Minecraft survival mode" Would be easier if P wasn't emeralds and S (iirc?) wasn't diamonds. Some dedicated soul would still do it though.
14:45 you can use retextured blocks. So you would only need to retexture once and then just place blocks. Easier keep an index on the corner of the screen with "block youre facing = pentomino" and just highlight what youre looking at.
Once you come back to polyominoes, you should look into hex-based pentominoes. (For clarity, use hexagonal tiles instead of square tiles to form the pentominoes. (I think there are 18 of those on a 2D plane, but I only tried to figure them out in my head.)
sort of ironic that the torus q was formed by l or y if you thought there were 38 solutions, but here, it's an addon to everyone's favorite 12 pentominoes. Also formed by N to spell nyl... now if only the O pentomino existed... then we could spell NYLON using two N-pentominoes, or NYLOFF using two F-pentominoes...
You should put item frames pn the inside of your minecraft visualizations so you can still see through it but if you add a grey block you will see the walls more easily.
Something i think would be cool (and something i have done myself already) is connecting dominoes so that all the pieces of a number connect (while obeying domino rules). The maximum you can do in 2D is 4. In 3D i managed to do 6.
8:15. Sorry to be a massive nerd but technically it’s called a Euler diagram not a Venn diagram. The reason why is because not all regions are connected. Edit1: also do 4-hypertorus next
NOTE: Amazingly, despite there being a month of time between working on this video, the 3x3x3 and 4x4x4 pentacube pathfinding solutions were both beaten AFTER I rendered this video, but BEFORE I uploaded it. Both were beaten by a single cell, which is pretty wild.
Really funny
lol
Alright I’m making a Blueprint for Hexomino Facts GET UP HERE DECKARD
Try 4 dimenional
@@Joshplays-Reccomendations already done up to 3x3x3x3 I think
Instant Carykh feel to the videos (Very good thing) keep up the good work!
5:15 they even got the Carys
Ironic since Carykh commented on the first episode
20:00
of course it's always the X pentomino to bring it home, just like in the entire series, what a legend for somehow turning into its letter form and taking over the whole board (also hexomino facts gonna be hype once you figure out all those names)
⬛️🟨🟨⬛️
🟨🟨🟨🟨
this hexomino should be former english letter thorn, change my mind
@@thelollykitty if we're going by single character names they should be single characters on a standard keyboard. thorn isn't on most keyboards unless you're icelandic or actively use thorn for other reasons, so it would be best to just use the standard letters and numbers everyone already has access to
We have A-Z and 0-9
Well well well
Time for pentatesseracts
Actually thr series would end with pentatesseracts, as anything above that would only contain the same penta-things as before, since there's a maximum of four different directions you can take using 5 cells
What about hexatesseract?
@ sounds very fun indeed
@@diegonalsbut you could orient and rotate them still in higher dimensions. Until some much higher dimension
there would be 1 new one i tihnk being the * pentesseract
fun fact: there are exactly 26 4d pentominoes (pentatesseracts), meaning there's exactly one for each letter
the new ones in 4d are O, C, and D
I wanna see!
@@Intergalacticprismaticcreature if you go to the spreadsheet in the description and click on the "pentomino cubes/tesseracts" link (third one from the top), that one has every 3d and 4d solution so far, along with a picture of the 3d and 4d pentominoes
obsessivr compulsive disorder
@@Intergalacticprismaticcreature good luck seeing them
@@alesonbrjk i am 4d creature 👽
I can't wait for 4D pathfinding
ah yes
Hell yeah my 4³ solution came in even though it was beaten 🔥
This is super well done again! I hope that you'll periodically make update videos for some of the coolest new pentomino shenanigans/updated records for the existing ones, as even though I'm definitely not smart enough to figure out these on my own (haha!) I would love to see the community's continued work!
I might tbh! A lot of the stuff from all the videos are outdated now as better solutions have been found, so I think in the distant future I might do another update video once new better solutions stop being found. That would not be for a really long time though, as to give as much time as possible for people to find even better solutions for many of these boards
@@v.deckard narnia
What a way to end the pentomino pathfinding series. This had me hooked from the start. Awesome stuff man!
Can't wait to pathfind on a 3-torus!
Thankkkk u soooo muchhhh
This morning i watched all the videos and im so happyyy that u dropped the 4 todayy ❤❤
19:32 - Yay I'm there
More new cube boards stuff:
5x5x5 has been improved to 55
6x6x6 has been improved to 80
I'm guessing it's the bottom layer with the 6x6x6 because it looked pretty open.
is there somewhere I can find these solutions?
@@blockshift758it already used every piece
Minecraft path findings are a genre of videos i didn't know i loved ^_^
2:56 MOM LOOK! IM ON A DECKARD VID!!! :DD
didn't expect to see you here :P
and on 2^8 !
Yoooooo
Yay a young person who doesn’t use emojis
Actually, for the pentacube pathfinding, those split layer diagrams on the right are quite understandable for me. This is a similar to how Lonpos presents those pyramid puzzles - they have split layer diagrams too.
These split layer diagrams work well for 4D too.
I love the pentomino series.
It has been so much fun :3
Here's a unifying framework for thinking of all these different varieties you have come up with (2d, 3d, torus, cube faces).
I think the correct generalization is a graph G as the "space", and subgraphs with 5 vertices as the "pentominoes".
The problem can then be posed as, given a connected graph G and a beginning and end vertex x and y, maximize the distance from x to y by removing a sequence of pairwise non-isomorphic k-vertex subgraphs from G.
Under this definition the weird corner cases and loopy cases from the cube and torus count as distinct new pentoninos.
i've been on a bit of a bejeweled binge lately so this got me thinking of what a match 3 game would be like if it were in a cube instead of on a flat 2D plane lol
Much more confusing.
@@Iam1Person i've actually been thinking about it more and it might work better if it were in a 4x4x4 cube and you only had to match 2 gems instead of 3 lol. that'd drastically simplify it i think... i hope...
So cool!!! Exited for whatever you do next!
YES!!!!! Wait the series is over NOOOOOOOOOOO!!!!!
6:50 the A tetracube actually has a rotational symmetry, going trough a side instead of a corner
Okayy , so I know what I'll build next on the server with my friends
I was one of the first 10,000 viewers on this video
Also, this series inspired me to make my own google sheet called "ominoes" and share it with my classmates
AHHH I WAS SO EXCITED FOR THIS BUT I FORGOT
13:38 i adore the walkthroughs
Fun Fact, 2x2x2 Pentacube Pathfinding IS possible, but all you need is the Q Pentacube, which gives us a path of 3 cells.
It’s sad this series HAS come to an end and im soo saad RECONTINUE IT!!!!!!!!!
Next step:3d hexominos
Later step:4d pentominos
3:43 very readable text
very
well now we dream of “5d chess battle advanced with multiverse time travel pentomino pathfinding”
Cant wait for the pentatesseract video!!
can't wait for some big mathematicians to discover the series and write a paper with weird symbols in which they prove and generate the paths for n-dimensional n-minos in a n-dimensional grid
actually it would be n-dimensional m-minos in an o-dimensional grid
FYI, spectator mode could be pretty helpful for any further visualizations where you need to travel through spaces smaller than the player. It's probably clearer to have the scaled up version so you don't phase through the walls as easily, but you could also use the scrollwheel to reduce the speed you move in spectator mode and still have a plesent experience. I'm loving the videos, though, btw!
I wanna have a minecraft house in one of those pentacube puzzles
"Where did that fifth cell go?"
It went to go develop the Scribblenauts franchise.
6:22 Actually, M has 2 axes of symmetry. You can make it diagonally, slicing between the 2 sticky-outy nubs
How did you made me love 5 square cells attached to each other in different ways
X and I casually being the absolute GODS of symmetry
It would be cool to see just the path that the pentacubes make in 3D. In minecraft this would mean that the air blocks become solid and the non-air blocks become transparent.
YESSS MORE PENTOMINO CONTENT 💕💕
First tpot 14, then this? This day can't get any better,
There is one way... For Geometry Dash update 2.207 to release on mobile!
*snap*
So to clarify, this one's going in r/suddenlyBFDI
And time for the 7:00 with object Unicode 1 (NOT 1A) is here
I started beatboxing when he was mentioning the pentacubes for the 6x6x6
Ideas: Klein Bottle pentacube pathfinding, hypercube surface pentacube pathfinding, and hyperpentacube pathfinding! (No idea how these would be visualised though)
YAYA, PART 4 IS HERE 🔥🔥🔥🔥
🥵🥵🥵🥵
@NmpPnm lol
"I dare someone to build this structure in Minecraft survival mode"
Would be easier if P wasn't emeralds and S (iirc?) wasn't diamonds. Some dedicated soul would still do it though.
"Im Going Into Minecraft For All" BRUH I WANTED TO SEE THEM WITHOUT MINECRAFT!!!!!!!!!!!!!!!!! **Gets A Gun**
We're in a golden age of mathematics.
14:45 you can use retextured blocks. So you would only need to retexture once and then just place blocks.
Easier keep an index on the corner of the screen with "block youre facing = pentomino" and just highlight what youre looking at.
10:28 bro sounded like carykh for a moment
Can't wait to pathfind on a 3x3x3x3 Hypercube!
I am almost certain this man will talk about Polyiamonds and Polyhexes at some point
you're starting to sound more like carrykh
Once you come back to polyominoes, you should look into hex-based pentominoes. (For clarity, use hexagonal tiles instead of square tiles to form the pentominoes. (I think there are 18 of those on a 2D plane, but I only tried to figure them out in my head.)
I was thinking about this too
Well, Congrats to the S Pentacube for being in every solution in 3d.
8:16 tpot credits
fr
small tip: you can use mods to force the player model to "swim" which makes it possible to traverse 1x1 spaces making the larger models unnecessary
can't wait for part 5: pentomino pathfinding hexomino edition
who's gonna tell her
not me
Never have I been more upset to have aphantasia. Even seeing the cube in real time it's breaking me brain.
more *mino content wooo
Haven’t watched but it’s peak
19:24 shouldn't the 1 and 2 be switched in the 5x5x5 pentacube pathfinding net?
Your "venn diagram" of which tetracubes are in each pentacune was actually an euler diagram
Great
Now 4 dimensional pentatesseracts now. :)
My next Meet Your Maker base is gonna go crazy
sort of ironic that the torus q was formed by l or y if you thought there were 38 solutions, but here, it's an addon to everyone's favorite 12 pentominoes. Also formed by N to spell nyl... now if only the O pentomino existed... then we could spell NYLON using two N-pentominoes, or NYLOFF using two F-pentominoes...
part five: polytominos
using pentominos and tetrominos together to make weirder boards
Don't worry about the diagram, JacknJellify uses a diagram like that in the credits
This is a good video 👍
I have gotten so attached to these pentominos and they are just cubes
people be talking about 4d pathfinding but what i wanna see is hyperbolic geometry pathfinding
Now do 4d pentatesseracts.
I want the larger 3D pathfindings to be big playgrounds ❤
You should put item frames pn the inside of your minecraft visualizations so you can still see through it but if you add a grey block you will see the walls more easily.
missed oppurtunity to make torus q and cubeface q the same color
Not me reading the title as cube facepainting 💀
Something i think would be cool (and something i have done myself already) is connecting dominoes so that all the pieces of a number connect (while obeying domino rules). The maximum you can do in 2D is 4. In 3D i managed to do 6.
i feel like someone could make a maze out of these pentominos, probably in minecraft
8:21 *equips nerd glasses * Uhm, *ackshually*, that's an Euler diagram.
next: 4D pentominoes
When you brought out Minecraft
Me: happy happy happy happy happy happy
2:57 not anymore
so the P-monstrosity is technically a tetromino on a cube-shaped board...
it can be formed by T or the-
Welp. My yt recommended me this and I'm gawking
Aight but like 4D pentominoes when
What if we allow for repeat pentominoes?
Next - sextominoes, sextacubes, septominoes, septacubes, octominoes, octacubes, nonaminoes, nonacubes, and finally decaminoes and decacubes
Now do pentacube path finding on the surface of a 4D hypercube.
I never comment this much but I have so much to say 😅
6:32 MSG THE KING OF FLAVAH
11:00 you could have used wool blocks for a more "uniform" look
8:21 i have a similar Venn diagram in my notebook but 2d hexominos
8:33 about half of the E pentacube (in the A tetracube group) does not show up.
2:05 the *[REDACTED]* shape it exists and doesn’t exist at the same time
The Schrodinger's Pentomino
For April fools could you do monomino facts
19:45
Please call the olive hexomino with a 3x by 5y bounding box "Rutherford B. Hayes' Hexomino" for no reason
19:32 im in the video!!!!!
the goat
diapentomino ( diagonal pentominos) pathfinding
could make a fort out of them 😅
8:15. Sorry to be a massive nerd but technically it’s called a Euler diagram not a Venn diagram. The reason why is because not all regions are connected.
Edit1: also do 4-hypertorus next
YAAAY