Pentacubes & Cube Face Pathfinding

[@v.deckard]

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.

[@Breuhh]

Really funny

[@aykarain]

lol

[@ElijahsAnimationChannel]

Alright I’m making a Blueprint for Hexomino Facts GET UP HERE DECKARD

[@Joshplays-Reccomendations]

Try 4 dimenional

[@Breuhh]

@@Joshplays-Reccomendations already done up to 3x3x3x3 I think

[@DominatrusAndWilliamRyong]

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]

⬛️🟨🟨⬛️ 🟨🟨🟨🟨 this hexomino should be former english letter thorn, change my mind

[@cater_piler]

@@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

[@haraldmbs]

Instant Carykh feel to the videos (Very good thing) keep up the good work!

[@boyonyacerus]

5:15 they even got the Carys

[@dootnoot6052]

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

[@Intergalacticprismaticcreature]

I wanna see!

[@dootnoot6052]

@@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

[@lailoutherand]

obsessivr compulsive disorder

[@alesonbrjk]

@@Intergalacticprismaticcreature good luck seeing them

[@Intergalacticprismaticcreature]

@@alesonbrjk i am 4d creature 👽

[@MemeAnt]

Well well well Time for pentatesseracts

[@diegonals]

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

[@ronalddavidrojas5795]

What about hexatesseract?

[@MemeAnt]

@ sounds very fun indeed

[@kylezdancewicz7346]

@@diegonalsbut you could orient and rotate them still in higher dimensions. Until some much higher dimension

[@abdijabarkhalif]

there would be 1 new one i tihnk being the * pentesseract

[@randomlol-ya3063]

I can't wait for 4D pathfinding

[@mxsteri0]

ah yes

[@Breuhh]

Hell yeah my 4³ solution came in even though it was beaten 🔥

[@h3nry_s71ckm1n]

Can't wait to pathfind on a 3-torus!

[@beagle_uah]

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!

[@v.deckard]

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

[@GiyeokFan1997]

​@@v.deckard narnia

[@ValkyRiver]

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.

[@BillelAktouf-pz7bc]

Thankkkk u soooo muchhhh This morning i watched all the videos and im so happyyy that u dropped the 4 todayy ❤❤

[@PotatoImaginator]

Minecraft path findings are a genre of videos i didn't know i loved ^_^

[@lock_ray]

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.

[@gpisthebest]

What a way to end the pentomino pathfinding series. This had me hooked from the start. Awesome stuff man!

[@NikoThePancake]

I love the pentomino series. It has been so much fun :3

[@wun_zee3599]

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]

Much more confusing.

[@wun_zee3599]

@@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...

[@lego_by_leo]

19:32 - Yay I'm there More new cube boards stuff: 5x5x5 has been improved to 55 6x6x6 has been improved to 80

[@blockshift758]

I'm guessing it's the bottom layer with the 6x6x6 because it looked pretty open.

[@Randomcelesteenthusiast]

is there somewhere I can find these solutions?

[@The360MlgNoscoper]

@@blockshift758it already used every piece

[@lr0dl012]

2:56 MOM LOOK! IM ON A DECKARD VID!!! :DD

[@xetto]

didn't expect to see you here :P

[@H_fromDiscord_real]

and on 2^8 !

[@betankreeper]

Yoooooo

[@antoniofigueroa887]

Yay a young person who doesn’t use emojis

[@diegonals]

6:50 the A tetracube actually has a rotational symmetry, going trough a side instead of a corner

[@bearcub7681]

YES!!!!! Wait the series is over NOOOOOOOOOOO!!!!!

[@MELoNIKASZ_.................]

Okayy , so I know what I'll build next on the server with my friends

[@SilverMoon-rr9fo]

So cool!!! Exited for whatever you do next!

[@PeriodicTableLover2]

19:24 shouldn't the 1 and 2 be switched in the 5x5x5 pentacube pathfinding net?

[@nmay231]

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!

[@MasterMal]

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

[@milkb4thecerealgames]

It’s sad this series HAS come to an end and im soo saad RECONTINUE IT!!!!!!!!!

[@justineezekielbolivar]

Next step:3d hexominos Later step:4d pentominos

[@kengyangtan]

AHHH I WAS SO EXCITED FOR THIS BUT I FORGOT

[@christopherscott7287]

Fun Fact, 2x2x2 Pentacube Pathfinding IS possible, but all you need is the Q Pentacube, which gives us a path of 3 cells.

[@Alex-ke2ht]

I wanna have a minecraft house in one of those pentacube puzzles

[@aikorrana]

Ideas: Klein Bottle pentacube pathfinding, hypercube surface pentacube pathfinding, and hyperpentacube pathfinding! (No idea how these would be visualised though)

[@AgainstMyBetterJudgement]

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.)

[@quadruplay9788]

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

[@Green24152]

actually it would be n-dimensional m-minos in an o-dimensional grid

[@justbrix3458YT]

6:22 Actually, M has 2 axes of symmetry. You can make it diagonally, slicing between the 2 sticky-outy nubs

[@ZilchZilch11]

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.

[@bugorgans]

YESSS MORE PENTOMINO CONTENT 💕💕

[@quadruplay9788]

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

[@calvinbarbanell2449]

8:33 about half of the E pentacube (in the A tetracube group) does not show up.

[@xaigamer3129]

8:16 tpot credits

[@undefined6512]

"Where did that fifth cell go?" It went to go develop the Scribblenauts franchise.

[@Intergalacticprismaticcreature]

First tpot 14, then this? This day can't get any better,

[@kidkrom9427]

There is one way... For Geometry Dash update 2.207 to release on mobile!

[@WaterOnTheHill-xp3yx]

*snap* So to clarify, this one's going in r/suddenlyBFDI

[@Kguy-r6e]

And time for the 7:00 with object Unicode 1 (NOT 1A) is here

[@aykarain]

9:49 shouldnt the path start from the middle cell, which also increases the length by 1?

[@pugza1s731]

rise one cube. go right right one cube. 4 becomes 3 lowering the total path length by 1

[@saltayjek0046]

what about hyperbolic pentominos

[@blockshift758]

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.

[@F1e308]

What about pathfinding with only one kind of pentominoes?

[@abxy_real_official_since2020]

X and I casually being the absolute GODS of symmetry

[@HaraceHavoc]

We're in a golden age of mathematics.

[@hysda80]

I started beatboxing when he was mentioning the pentacubes for the 6x6x6

[@pugza1s731]

can i ask for the list of materials needed for the 6x6x6?

[@Ppdm2011]

Can you release your pentomino image pack?

[@Roaxial]

Your "venn diagram" of which tetracubes are in each pentacune was actually an euler diagram

[@d1scocubes]

Can you make the pentacubes out of glass as well?

[@deadakus]

Never have I been more upset to have aphantasia. Even seeing the cube in real time it's breaking me brain.

[@SpacetimeHTWML]

For April fools could you do monomino facts

[@Therevengeforget]

"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.

[@ratewcropolix]

3:43 very readable text

[@aykarain]

very

[@fuuryuuSKK]

more *mino content wooo

[@AMudkipAmongUs]

Haven’t watched but it’s peak

[@Ayembee1103GD]

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...

[@breadgirl]

4D?

[@Blackfromstickworld]

Can't wait to pathfind on a 3x3x3x3 Hypercube!

[@echo5172]

Is it possible to expand this methodology up to 4d?

[@ExzaktVid]

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.

[@mrhangertv1829]

I am almost certain this man will talk about Polyiamonds and Polyhexes at some point

[@phantomdergwulf]

you're starting to sound more like carrykh

[@4U70_DeadAuto]

Don't worry about the diagram, JacknJellify uses a diagram like that in the credits

[@tempehph3364]

8:21 i have a similar Venn diagram in my notebook but 2d hexominos

[@Negreb25]

YAYA, PART 4 IS HERE 🔥🔥🔥🔥

[@NmpPnm]

🥵🥵🥵🥵

[@Negreb25]

@NmpPnm lol

[@Toy_Bonnie_FNaF2]

What about cuboids?

[@blueguns15000]

well now we dream of “5d chess battle advanced with multiverse time travel pentomino pathfinding”

[@VeryMonkelol]

10:28 bro sounded like carykh for a moment

[@Insertagoodusername]

Aight but like 4D pentominoes when

[@X3m.Gaming]

wait wheres the 4d path making?

[@terabyte6903]

oh no

[@octopus_72]

how can it be over when we haven't gotten 4d pentominoes :(

[@ElectricalIntersection]

Or 5d

[@v.deckard]

3d pentomino pathfinding was already hard enough to visualize as is lol

[@octopus_72]

@@v.deckard 4d chess, 4d minesweeper... and we gave up on this ? 🥺

[@dootnoot6052]

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

[@Ayembee1103GD]

missed oppurtunity to make torus q and cubeface q the same color

[@m90e]

can't wait for part 5: pentomino pathfinding hexomino edition

[@tgr6273]

who's gonna tell her not me

[@8316WC]

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.

[@RobynAudiomancer2]

part five: polytominos using pentominos and tetrominos together to make weirder boards

[@JonisManci]

Well, Congrats to the S Pentacube for being in every solution in 3d.

[@sgtnerf-v2d]

What about triominoes

[@circumplex9552]

theres only two of them so it wouldnt be too interesting

[@AdrianLee-w7l]

This is a good video 👍

[@maungmaung6736]

Great Now 4 dimensional pentatesseracts now. :)

[@krocodile55]

Hmm... I wonder how hard it would be to turn the 6x6x6 pentacube pathfinding into a house.

[@schockocraft4897]

people be talking about 4d pathfinding but what i wanna see is hyperbolic geometry pathfinding

[@SerialDesignationF420]

Should we do Hypercubes?

[@SerialDesignationF420]

I can do the hypercube versions if you want

[@Ayembee1103GD]

so the P-monstrosity is technically a tetromino on a cube-shaped board... it can be formed by T or the-

[@tristinbell]

My next Meet Your Maker base is gonna go crazy

[@KBoden1973]

"Im Going Into Minecraft For All" BRUH I WANTED TO SEE THEM WITHOUT MINECRAFT!!!!!!!!!!!!!!!!! **Gets A Gun**

[@jstnrgrs]

Now do 4d pentatesseracts.

[@humanperson2375]

does this mean we need a minecraft creative mode server?

[@YourstruelyLoL]

2:57 not anymore

[@Revilo_Butnotreally]

I have gotten so attached to these pentominos and they are just cubes

[@theodriggers549]

I wanna do 7x7x7

[@EHMM]

the goat

[@blockshift758]

11:00 you could have used wool blocks for a more "uniform" look

[@melovesnoopy]

2:05 the *[REDACTED]* shape it exists and doesn’t exist at the same time

[@speedy5768]

I want the larger 3D pathfindings to be big playgrounds ❤

[@30IYouTube]

YAAAY

[@asheep7797]

19:45 Please call the olive hexomino with a 3x by 5y bounding box "Rutherford B. Hayes' Hexomino" for no reason

[@algotkristoffersson15]

Now do pentacube path finding on the surface of a 4D hypercube.

[@lolosharacarrot5507]

Next - sextominoes, sextacubes, septominoes, septacubes, octominoes, octacubes, nonaminoes, nonacubes, and finally decaminoes and decacubes