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)
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
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, 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.
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 A lot of the stuff from all the videos are outdated now as better solutions have been found, so I think in the distant future I might do another update video once new better solutions stop being found.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
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'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...
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 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
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.
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-Games already done up to 3x3x3x3 I think
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)
I can't wait for 4D pathfinding
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
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
Hell yeah my 4³ solution came in even though it was beaten 🔥
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 👽
X and I casually being the absolute GODS of symmetry
Instant Carykh feel to the videos (Very good thing) keep up the good work!
5:15 they even got the Carys
Can't wait to pathfind on a 3-torus!
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 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
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
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.
What a way to end the pentomino pathfinding series. This had me hooked from the start. Awesome stuff man!
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
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.)
Okayy , so I know what I'll build next on the server with my friends
Thankkkk u soooo muchhhh
This morning i watched all the videos and im so happyyy that u dropped the 4 todayy ❤❤
Minecraft path findings are a genre of videos i didn't know i loved ^_^
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...
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 love the pentomino series.
It has been so much fun :3
I want the larger 3D pathfindings to be big playgrounds ❤
8:16 tpot credits
It’s sad this series HAS come to an end and im soo saad RECONTINUE IT!!!!!!!!!
Next step:3d hexominos
Later step:4d pentominos
YES!!!!! Wait the series is over NOOOOOOOOOOO!!!!!
6:22 Actually, M has 2 axes of symmetry. You can make it diagonally, slicing between the 2 sticky-outy nubs
So cool!!! Exited for whatever you do next!
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
3:43 very readable text
very
AHHH I WAS SO EXCITED FOR THIS BUT I FORGOT
i feel like someone could make a maze out of these pentominos, probably in minecraft
YESSS MORE PENTOMINO CONTENT 💕💕
Try Triangle pentomonoes, that instead of squares, you replace them by Triangles.
6:50 the A tetracube actually has a rotational symmetry, going trough a side instead of a corner
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
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.
YAYA, PART 4 IS HERE 🔥🔥🔥🔥
🥵🥵🥵🥵
@NmpPnm lol
Well, guess the next one will be pentatesseracts 😊
Haven’t watched but it’s peak
Can you make the pentacubes out of glass as well?
10:28 bro sounded like carykh for a moment
Q AND R PENTIMENTO HAS RETURNED!!
more *mino content wooo
19:24 shouldn't the 1 and 2 be switched in the 5x5x5 pentacube pathfinding net?
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.
Neato! Now what's it like to navigate in 4D?
Don't worry about the diagram, JacknJellify uses a diagram like that in the credits
What about pathfinding with only one kind of pentominoes?
Next - sextominoes, sextacubes, septominoes, septacubes, octominoes, octacubes, nonaminoes, nonacubes, and finally decaminoes and decacubes
Never have I been more upset to have aphantasia. Even seeing the cube in real time it's breaking me brain.
what about hyperbolic pentominos
Aight but like 4D pentominoes when
can i ask for the list of materials needed for the 6x6x6?
part five: polytominos
using pentominos and tetrominos together to make weirder boards
the goat
Welp. My yt recommended me this and I'm gawking
This is a good video 👍
9:49 shouldnt the path start from the middle cell, which also increases the length by 1?
rise one cube. go right right one cube. 4 becomes 3 lowering the total path length by 1
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
next: 4D pentominoes
Should we do Hypercubes?
I can do the hypercube versions if you want
19:32 im in the video!!!!!
It's pentominover
YAAAY
6:32 MSG THE KING OF FLAVAH
Not me reading the title as cube facepainting 💀
Idea: 4D pentominoes
Hmm... I wonder how hard it would be to turn the 6x6x6 pentacube pathfinding into a house.
Is it possible to expand this methodology up to 4d?
diapentomino ( diagonal pentominos) pathfinding
8:33 about half of the E pentacube (in the A tetracube group) does not show up.
inecarfet :)
11:00 you could have used wool blocks for a more "uniform" look
Your "venn diagram" of which tetracubes are in each pentacune was actually an euler diagram
I wanna do 7x7x7
What about cuboids?
On the 5x5x5 they went 18 19 10 21 22
wait wheres the 4d path making?
9:10 maicra
1 hour ago
13:54 It shows 10 instead of 20
What about triominoes
theres only two of them so it wouldnt be too interesting
how can it be over when we haven't gotten 4d pentominoes :(
Or 5d
3d pentomino pathfinding was already hard enough to visualize as is lol
@@v.deckard 4d chess, 4d minesweeper... and we gave up on this ? 🥺
currently tesseracts that have solutions:
2×2×2×2 - 6
2×2×2×3 - 9
2×2×2×4 - 14
2×2×3×3 - 16
2×2×2×5 - 17
3×3×3×3 - 31
its funny that 6 by 6 by 6 has a path of 77, while the credit says ondra77
PENTOMINOOOOOOOOOOOOOOOES
bruh 3 hours ago is 6 am
does this mean we need a minecraft creative mode server?
9:39 pentacube pathfinding in minecraft
for some reason i wanna see trianglular pentominoes
The I pentomino could be considered a 1D pentomino, so there really are the same number of 2D and 3D pentominos: 1 1D, 11 2D, and 11 3D!
next up: hyperbolic pentomino pathfinding
(joke)
5D pentomino pathfinding with multiverse time travel
Sub 3 gang
Part 5
So, three letters without a pentacube... They are... C, D, and O
k looks like a, uhhhh, yeah, I won't say it
Now do 4d :ascending to heaven:
2:57 not anymore
Minecraft jumpscare