Oxford University Mathematician REACTS to "Animation vs. Geometry"
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- เผยแพร่เมื่อ 4 ก.ค. 2024
- Oxford Mathematician Dr Tom Crawford watches @alanbecker's "Animation vs. Geometry" for the very first time. Watch the original video here: • Animation vs. Geometry
*The copyright of the original video is the property of Alan Becker. The footage is shown here under a fair usage policy.
Watch Tom react to the first 2 videos in the series at the links below.
Animation vs. Math: • Animation vs. Math
Animation vs. Physics: • Animation vs. Physics
Watch Tom take a variety of high school maths exams from around the world on the designated playlist here: • Exams
Watch Tom on 'Numberphile' here: • Parabolic Mirrors - Nu...
Produced by Dr Tom Crawford at the University of Oxford. Tom is Public Engagement Lead at the Oxford University Department of Continuing Education: www.conted.ox.ac.uk/
For more maths content check out Tom's website tomrocksmaths.com/
You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.
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Get your Tom Rocks Maths merchandise here:
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Go watch the original video on Alan's channel so he'll keep making more amazing videos like this for us to enjoy: th-cam.com/video/VEJWE6cpqw0/w-d-xo.html
For additional references like name of that evil shape or the ideas you can watch alan's own reaction with his friend (link in the comment section of the animation video)
It’s a 4D hyper diamond
25:14 Well the attacking thing was a 4-D shape…
Paused to count. Yep, it's 24 vertices total with triangular faces. But it is not the Hyperdiamond! It's the weird one in 4 dimensions that doesn't have a lower dimensional analogon.
i watched 2 of your animations videp
Alan Becker really has made something special with his time on TH-cam. Amazing educational content, gripping and emotionally compelling narratives, awesome fight scenes, and all that with just stickmen and no dialogue whatsoever! It’s no wonder his videos get millions of views!
True
I don't know. I feel vs math was brilliant and inspired, the rest lacked depth. Kind of like star wars.
@@tinkeringtim7999nah
I've only seen the maths and science ones. All today as I'd never heard of it until this video. His other ones all looked like Minecraft vids so I haven't bothered with them
@michaelcolbourn6719 his video "Animation vs. Minecraft Shorts Season 3 - All Episodes (20-30)" is a masterpiece! it's a very well made story, I highly recommend it! Even if you don't play/know/enjoy Minecraft.
Little addendum for the stuff you missed:
- The thing attacking them is a 4D shape. Apparently it’s called a 24-cell.
- The Pythagoreas Theorem proof is also a proof for Φ + 1 = Φ². Specifically it said Φ raised to 0 plus Φ raised to 1 equals Φ squared.
- That bit makes the golden rectangle, and it pops up later during the pentagram battle.
- The dart shape is also part of the rhombic structure associated with the golden ratio, and Phi they did in fact make that shape to protect our stickman.
- You probably noticed, but I’ll still mention how the badass Phi army was creating all sorts of Φ shapes and lines to pelt the 24-cell. Absolute masterpiece.
- Phi army dropped some golden rectangles earlier, our stickman used them to create vertices that if you connect lines through, traces an icosahedron (it did this without Phi’s help, so proud)
- Phi then uses this to connect a dual one with area Φ², to create a bigger set of vertices to create the dodecahedron.
- Apparently if you put three dodecahedrons to the same edge you get that mirror effect or something, I honestly don’t understand that higher dimension explanation from the over-analysis either lol. The other shapes there are also the bigger and smaller 4D shapes, including the 600-cell forming a shadow in the mirror plane. Try and look for it, I’m sure you missed it. I did. Several times.
- The current crackpot theory is that:
Stickman arrives in math dimension > gets Euler’d to geometry dimension > falls off dimensional mirror into physics dimension > creates the entire universe with black hole time travel > Stickman is data and therefore immune to death by spaghettification > ??? New Animation vs. Education video yay
Here's a video that's got all that and prolly more.... th-cam.com/video/Nc2RPm0WhwI/w-d-xo.html
i'm hoping they do a atomic chemistry part as continuation of coming out of the black hole area and after that a molecular sized one that explores how different atoms react with each other and form bonds. then either go up the electromagnetic route into engineering or light theory or so(doing more more specific physics unrelated to speed) or into the dna and cell area and up the biology scale.
The 4D shape is also known as a hypercube. It's a theoretical shape that takes the idea that: a 1D line is made of two 0D points. A 2D square is made of four 1D lines. A 3D cube is made of six 2D squares. If we continue that logic, then a 4D hypercube is made up of a number of 3D cubes.
@@finian2 the hypercube is a different 4d shape that you can see at the end. it is not the one that is attacking.
@@dovos8572 huh yeah you're right. I assumed because at some points it looked almost exactly like a hypercube it was one, but looking at it again it has way too many lines.
"It can't be reasoned with, it can't be bargained with…it doesn't feel pity or remorse or fear… and it absolutely will not stop. Ever. Until you are dead. It's called... a 24-cell."
It doesn't think.
It doesn't feel.
It doesn't laugh, nor cry.
Ali it does,
From dusk 'til dawn,
Is make poor students die.
- a mathematician's cry
Great song :)
The 4D shape is called an Octaplex, which is the simplest of its names, and sounds oddly badass
Someone said, that it sounds like an awesome supervillain name.
There's also a lot of other names, I prefer Hyper diamond but there are others
Octaplex, 24-Cell, icositetrachoron, Octacube and others
Its also a hyper diamond if rotated towards the interface if regular (24 cell)
@@Nitram4392 are you referencing tyler folse?
If Dr. Octavius became a pro wrestler after his lab accident, he would have the Octoplex as his special move.
I think the "graph theory blob" is a 24-cell. This four-dimensional shape is difficult to understand because it has no analogue in higher or lesser dimensions. Or as HSM Coxeter states in the epilogue of his book "Regular Polytopes", the 24-cell is a shape that "stands quite alone". So as a story, perhaps the 24-cell was lonely, misunderstood, wanting friends. By the end of the video, TSC and phi have worked together to reunite the 24-cell with the other 5 convex regular polytopes, as a family. Very on brand for Alan's stick-o-verse.
can't believe that dnd dices are just the platonic shapes but magicified
except for the d10
@@nanamacapagal8342 pentagonal bipyramid
excluding the d10, because the d10 is an abomination that is a product of our broken numbers system :3
And the Destiny exotic engram
Mathematicians call them polyhedra,
Tabletop geeks call them dice.
Destiny gamers call them engrams
d&d geeks do not call an infinite plane of equal squares dice?
@@cewla3348 they do. But isn't nat-aleph cheating?
I think someone else mentioned it elsewhere, but the big evil thing is a 4D shape, specifically a 24-cell.
It's amazing how they used a 3D shape to trap a 4D being on a 2D plane.
Since TSC and phi are trapped in a 1D line, it would make sense to trap a 4D thing in a 3D shape.
@@wanwan_anderson therefore implying that the 4d thing isn't exactly flying, gravity is just affecting it in the 4th dimension
A 3D shape cannot trap a 4D being, because it can move on an additional dimension. It would be like someone using chalk to draw a circle around you on the floor and saying you are trapped when you can just step out of the circle.
@@SgtSupamanFrom the perspective of the 4D shape thing, couldn't it just take a step "sideways" (or whatever the 4d equivalent is) and escape?
@@RangeCMYK , yes, that is what I was saying. To a 4D shape, a 3D shape is 'flat' (its size is 0 in some dimension), so it is trivial for it to get out of the 3D shape, because the 3D shape never contained it in the first place.
petition to have Alan Becker collab with Tom Crawford for the next animation in this series
YES
lol yes
Now that is definitely i could get behind
Animations vs Tom Crawford 🔥🔥
hell yeah
17:03 For anyone wondering, it's called the Inscribed Angle Theorem
I’m still calling it the “Star Trek Logo Theorem”
@@TomRocksMathslol
My own personal theory is that the method Euler’s used to send TSC away actually split him - one went to Physics, one went to Geometry. The two are, for lack of a better term, happening “concurrently”. (Let’s ignore the ludicrous amounts of time it would have taken Physics to happen - Time doesn’t seem to hold sway in these, merely causality. Perhaps, since between Physics, math, and geometry, we’ve handled what I’d consider three of the four most fundamental concepts of reality, the next one will be the fourth - Time.)
The film theorists???
@Stakatakataka I mean, it's a theory about a film based at least partly on headcanon and supposition rather than fact, so I suppose its pretty Matpat-y, yes. :)
I took this idea from "Animation vs. Geometry - An Over-Analysis", apparently the oddly looking shape is called a "24-cell", a regular 4d shape that is considered to be a "4-D Platonic Polytope". The reason why it is attacking TSC and Phi is because it is the only shape, in their plane, that is not symmetrical.
The 4 colored platonic solids at the very end are referencing Plato's elements (fire, earth, air, water, Universe).
Correct me if I'm wrong, because I truly find Alan Becker's animation vs math/science to be really interesting. And I'm getting hooked by it.
I didn't get you? Is the 24 cell the only shape in 4D that isn't symmetrical?
@@ace9u No. It is the only shape in the video that isn’t symmetrical on all sides because it is a 4D object in a 3D world. We do not see 4D objects because we are 3D creatures seeing 2D objects.
Phi (Golden Ratio) is symmetrical whereas the 24 cell (in a 3D world) isn’t, which makes 24 cell the antagonist of this video.
the villain of the video isn't a graph its a representation of a 4d shape
I mean, that's still a graph.
The shape that was destroying everything was a four dimensional hyper diamond
If you're wondering about the dodecahedron-universe ending, this actually ties in to Plato's contribution to the platonic solids (plus the color scheme for the other 4 solids)
Plato assigned the solids different classical elements:
Tetrahedron = Fire (Red)
Octahedron = Air (White)
Cube = Earth (Green)
Icosahedron = Water (Blue)
Dodecahedron = Aether (Gold)
The inside of the dodecahedron is a 4-dimensiomal 120-cell comprised of 120 dodecahedra (go figure), so it might be the higher-dimensional equivalent of aether...
All the other 4d graphs are the remaining 4d platonic solids. In fact, the gold one orange stickman holds in their hand is the exact boss they were fighting against earlier: the hyperdiamond made of 24 octahedra (hence the octahedral artillery)
EDIT: got air and water backwards oops
that "graph thing" is actually a 4-dimentional shape called a 24-cell or icositetrachoron en.wikipedia.org/wiki/24-cell
whats next? animation vs chemistry? animation vs history? animation vs biology? animation vs geography?
probably chemistry
It is probably gonna be animation vs multiverse
Animation vs. Calculus?
@@morganansell4526 thats just vs math
@@oneleaf11 so was vs geometry
Honestly this man is amazing, always inspiring and carrying a happy smile. Currently in the process of doing my application for maths at Oxford, and I would not be in this position if not for Tom. Been an inspiration since day one and hope that you carry on what you do
8:20 let that sink in folks. Oxford Math phd forgot it. Not everything you learn in school is important- most of it is there on the chance some student finds it interesting and decides to pursue a career in that direction- so don't stress about it. Focus on what's interesting to you, the topic that you enjoy, and do just enough on everything elese. Don't let yourself burn out by age 18...
Yess!! I’ve been checking my feed every day for this video!! Love your reactions to these animations, they’re really well explained and you show such appreciation for the fundamental laws that create our universe. Can’t wait to see your reactions to Alan’s future work with this series :D
A point becoming a line is going from 0D to 1D, not 1D to 2D. It doesn't become 2D until the stick figure comes out of the line.
In the most genuine and non-weird way possible: I love the way you love maths. I have been actively looking for your take since it first came out. Thanks for sharing your insights 😀
Fun fact, the platonic solids were actually demonstrated in increasing order of vertices as the tetrahedron has 4, the octahedron has 6, the cube(hexahedron) has 8, the Icosahedron has 12, and the dodecahedron has 20. It's actually funny to note that objects after the tetrahedron are pairs with the vertices and faces swapped. so if we were to discover another layer of these solids it would probably follow a similar pattern of the swapping and would thus be discovered in a pair.
Actually the dodecahedron has 12 sides, the icosahedron has 20
A cube has 6 sides and an octahedron has 8
@@jakkakasunset5485 oh yeah I didn't notice that too
@@murmunster1761its number of vertices, not faces. cubes and octahedrons are duals, so a cube has the same number of faces as an octahedron has vertices, and vice versa. this is true for the icosahedron and the dodecahedron as well. you can constuct the dual of a polyhedron by flattening each vertex until the new faces meet, or by adding a vertex at the center of each face and connecting them to form a new polyhedron. for the tetrahedron, its dual is itself (you can also find the dual of a polyhedron by reversing its schläfli symbol, for example a cubes symbol is [4,3] and an octahedrons is [3,4])
You are correct but if you pay attention I am also correct, as I wasn't talking about the number of faces or as you are calling them "sides." I was talking about the vertices or as you might call them convergent points... heck of a way to miss the point. Especially considering talking about geometric points...
thank you for explaining everything! after watching it, i figured it was about the golden ratio. Explaining the different fractals and why the golden ratio is mathematically intresting was truly nice to learn about.
These two guys... Alan Becker & Tom Rocks
This’ll be fun!
I’ve been waiting for the reaction videos just because I like watching the reactions of experts.
I’ve already watched the over analysis so I’ve probably become a geometry nerd over the week, but I still want to see your academic reaction lmao
I was waiting patiently for this >.
Sameeee
In a couple of years we'll be getting Animations vs Noncommutative Rings and it'll still be great
Intro correction: that would be 0 dimensions to 1 dimension (zero-D to one-D).
been waiting for your reaction on this!! your videos are so great :)
It is so validating to hear your struggles with circle theorems, I had the same experience after finishing my math degree lol
Alan Becker brought back so much Knowledge that I had thrown away.
With your explanations, everything that I couldn't grasp before, is now easier to understand. Thank you.
I previously made this comment on another math channel, but I like to conceptualize the fourth dimension by analogy to something from the book _Flatland_ (which I'm sure we've all read). The protagonist tries to explain the third dimension as, "Up, but not north." I think of the fourth dimension as, "Out, but not up." Here, the tesseract 3D "shadow" is a good analog, despite what Matt Parker says 😝.
I've gained a greater understanding and appreciation for the geometry in Alan's video because of this guy. Learning about the platonic solids makes the climax SO much more hype!
I love watching mathematician's raw reactions to these animations!
This is what i've requested 5 days ago in my comments at your reaction to Animation vs Math
Thx for making this vid its funny and cool at the same
I love Geometry Dash.
i looove gd cologne
FIRE IN THE HOLE🔥
🕳️
Geometry dash 🗣️🔥🔥
We saw 1d, 2d, 3d and 4d shapes. What I found interesting is that when attacked, stuff showed the menger sponge underneath, which has a fractal dimension of between 2 and 3
The moment that video dropped I was looking forward to your reaction and explanation.
I swear tom I didn't know id fall in love with math. debunking Alan's animations really made me wanna know more about math and geometry. also you're kind of a genius lol
oh snap, lets go 3rd part
i was waiting for this thank you
that "graph theory" thing looks like its rotating in 4D. When it was shooting, it shot what looks like the 3D "faces" of the 4D shape.
I wonder if the villain is themed around the concept of irregularity. It seems like that would make sense given the heroes are fighting it with regular shapes. Hopefully a sequel could have them reconcile their differences and find the beauty in irregular shapes.
15:01 - “to allow orange stick man to pick up the dots…”
How did you know he would pick them up at all? I think *his video is ahead slightly of the one we see*
You’re the only reaction that matters to me thank you for being awesome
aaaa i got so freaked out and got so scared by looking at just the simple fractals
The evil graph theory blob is a evil 3D shadow of a 4D hyperdiamond (2D if you count the screen). Source: the video in the description of the original video
I started with "nuclear physicist reacts" and watched like a dozen different high-end-smart people since. You're the only one I actually subscribed to. I love your energy and the explanations.
Keep up the good work.
Welcome to the community :)
I COMMENTED ON THE VIDEO "can't wait for tom rocks maths to react to this" WHEN IT CAME OUT AHHHHHHHHH!!!!!!!!!!
The two kites constructed from the golden ratio were selected from the P2 and P3 non-periodic Penrose tilings, hence their relationship to the golden ratio.
The square areas for the Pythagorean theorem part demonstrate one + phi = phi^2.
And as many others have stated, the antagonist is the 24-cell, the only 4D Platonic solid without a perfect 3D analog (the cubeoctahedron and rhombic dodecahedron, taken together, best capture its essence).
As something as Universally simple as a stick figure, I feel like many of us got our enjoyment and extention of stickfigures creations from Alan Becker and his usage of his skills and knowledge integrated into his fast learning stick figures
Now that I watched this video again, I feel like I found a mistake.
At 6:47 here we see the triangle being rotated by 150, but isn't that 120? I mean the angle on that side of the triangle is 60, so it should be 120 rotation instead.
yay been waiting for you :)
I like how i recognized the 4d rotation of the "graph theory blob" instantly lmao
I think all the platonic solids are referencing the 5 elements too, Fire, air, earth, water, and Aethos in that order, due to the colour that they glowed when the 24-cell was trying to break through them
this guy teaches 10x better than my math teacher
In some languages, this illustration of Pythagorean theorem is called Pythagorean Pants, lol
i wish youd mentioned the other regular polyhedra..... theyre so my beloved
The higher dimensional monster can be thought as the 24-cell
I asked my teacher to show animation vs math to my class and they loved it
I highly recommend (to fellow watchers here) watching jan Misali's video on the "48 regular polyhedra" which is a beautiful example of how the "three easy rules" for the platonic solids actually lack proper constraint. To them we simply add the rule(s) of being finite, closed, strictly convex, self non-intersecting polyhedra to get the five platonic solids we know and love, but relaxing these restrictions give us a wonderful world of highly symmetric objects that still lie within the "spirit" of the platonic solids, so to speak!
Yeah, truly awesome video
Definitely an 😃 amazing video! I shall watch it again!
In the physics video When there are two orange Stickman, you can see One of them holding an Interdimensional device that kind of looked like the thing he trapped in. My other thought is that The space cowboy Was transported into the shape.
Yep, I have confirmed that one of the orange stick men had a word shaped thing.
14:03 Menger Sponge is the 3d version of the fractal in the video, called a Sierpiński carpet.
I was gonna say the same thing because i got confused when he called the 2D one the 3d ones name lol
God I absolutely hate circle theorems! Im an undergrad student and couldnt remember them either feeling dumb as its GCSE as you said, glad you still have the same problem 😅
I read the "graph theory blobs" as 4-d regular polytopes
I've read somewhere, that what TSC is doing is constructing an icosahedron using mutually orthogonal golden rectangles. It has something to do with the vertices of these rectangles that relate to the icosahedron (d20) but I'm not sure.
26:00 I just visualise 4d objects as stuff that has edges in other slices of time, if you're not in the right slice of time then you can't see those edges. If an edge has vertices in 2 different slices of time then you see it fade out due to it moving through time and you can only see the chunk of it that's close to your slice of time.
We really a collaboration with Tom and Alan
Elemental correlation to the Platonic solids shows through as well, Red = Fire, Grey = Wind, Blue = Water, Green = Earth, and Gold = Ether
gallium gonzolium did a pretty good job. Well done Dr. Tom
something cool that was there is that the platonic solids are linked to different elements, the tetrahedron is linked to fire, the octahedron is air, cube is earth/rock, the icosahedron is water and the dodecahedron is metal or in the animation just golden for phi
(i might have got some things wrong let me know if i did) something i forgot they shine the color of the elements fire/red air/gray earth/green water/blue (metal/gold probably not tho)
At 26:49 there are 4D 'platonic solids': an hypertetrahedron and an hypercube (teseracton) and maybe others regular 4-polytopes
Yes!
12:43 this has probably been said before but I'm pretty sure that the 2D version is the sierpinski carpet, the 3D version is called the menger sponge
21:35 By the first rule you mean it has to be convex and physical, not just 3D. You can use software to construct a 3D polyhedra with polygons of five sides, where each is a shape of a five-ray star, not just pentagon.
did you hear about 4D Golf? Because you said it is hard to visualize more dimensional Space and this game does exactly that by switching between various modes. It is a marvel of game design and geometry.
Reminding me of my Foundations of Advanced Mathematics professor from college, if he ever heard us mention "Straight Line", he'd let out a loud squeak since the definition of a line is that it's straight. He basically conditioned us into using the "proper" definitions.
17:04 Star Trek Logo Theorem is now my head cannon name for Euclid's inscribed angle theorem. 😁
The golden hand-glider (drawn by TSC and phi) is a dart shape composed of two Robinson triangles. This dart shape (and the kite shape drawn at 17:50) are used in the second type of Penrose tiling. For pretty diagrams, look up "Penrose tiling" in wikipedia.
Regarding to 4 dimensional space, I always like to think of it as time, it is because similar to Frames Per Second on a game, the way how smooth we move through time is what i think as 4D
Looks like everyone but Tom spotted that the attacking shape is 4D...
The sound work was incredible, even for an Alan Becker original
1:02 A dot is zero dimensions. A line is one dimension. So it is: "Which is like 0-D to 1-D"
1:21 It only became 2-D when orange stickman broke out of the line.
12:42 THATS A SIERPINSKI CARPET WHAT ARE YOU TALKING ABOUT
From what google has told me, the Menger Sponge is the 3D representation of the Sierpinski Carpet
I remember drawing fractals on ms paint in schoo, it's actually really fun and easy to do 😂 At one point tho, the fractal becomes too big and there's a finite limit to how much you can increase the canvas 😂
27:25 that was happened in interstellar movie when goes into black hole and goes to higher dimensions
I wonder if at the end, where it all statts again, the line is still below. Suggesting that was all taking place on the same number line, and theres an infinite number of parallel lines and that story will repeat infinitely.
21:42 You need to specify that your polyhedron is convex in order to obtain only the platonic solids. jan misali made a video some years ago about how many polyhedra there are if you don't. (The Kepler-Poinsot polyhedra are only the beginning.)
graph theory was a tesseract 4th dimension
its a hyper diamond
Youre statements about the platonic soilds reminded me of a video Id love to see you react to. "There are 48 regular polyhedra" by Jan Misli. Its a great video about a very strange part of math
The 4D Shape attacking The Second Coming and Phi is a 4D Hyper Diamond or just 24-cell
the mandlebrot set is the dragon curve thing you talked about.
I expected Tom to mention Duals of Polyhedra. When Stickman and Phi connect the centers of the faces of the octahedron, they create a cube. Vice versa, connecting the centers of the faces of a cube creates an octahedron. Dodecahedron and icosahedron are similarly each other's dual, but tetrahedron is special, because it's its own dual.
I’m holding out hope for an Animation Vs Crop Circles
Seeing the orange stickman appear many times through out the "4-D" space made me think of something I hadn't befote. It made me wonder "could it be that by going into a higher dimension everything in lower dimensions can be observed all at once?" Maybe at 4-D space everything in a 3-D space could be seen from all sides at once?
The graph theory blob when it was inside the dodecahedron hall of mirrors 26:49 (non-euclidian geometry reference) was met by other graphs, I think they were the 5 cell, Hypercube, and 600 cell, I think that'd make the graph theory blob the 24 cell, we met the 5 cell in it's graph form too. we don't seem to meet the 16 or 120 cell 4D polytope
The hall of mirrors IS the 120-cell. The hypercube/tesseract is the 8-cell, so they're all represented.
@@davidkeith3920 sorry I meant 16 cell was the one I didn't see but good catch on the 120
it leaves behind a 2d version mengers sponge called sierpinski carpet. 12:45
I heard another guy call the thing that is attacking a 4th dimensional thing.
Also, i can kind of say that a 4th dimensional ball is still a ball. However, the same ball when it crosses the 4th dimension into the 3rd dimension will look to us as a ball that can change size from small to large back to small till its back in its own dimension.
That reminds me of a topic in my Abitur. It was the verbal test in math. (That stick to me despite it being more than 25 years ago.) To say it bluntly it was forms evolving with dimensions.
We had looked at two forms: The triangle and the square.
Triangle:
When we are at o dimensions, we have 1 point, 0 lines, 0 faces and 0 rooms. Its a dot.
In 1 dimension, we have 2 points, 1 line, 0 faces and 0 rooms. Its a line.
In 2 dimensions, we have 3 points, 3 lines, 1 face and 0 rooms. Its a triangle.
In 3 dimensions, we have 4 points, 6 lines, 4 faces and 1 room. Its a tetrahedron.
Two things are to be known: In order from one dimension to the next we draw one point in the new dimension and connect it to all other points. And these numbers look like pascal's triangle, without the leading 1.
With A points, B lines, C faces and D rooms the next would be 1 + A points, A + B lines, B + C faces and C + D rooms.
So in 4 dimensions it would be 5 points, 10 lines, 10 faces, 5 rooms and 1 ??? (body of the fourth dimension).
Square:
In 0 dimensions we have again 1 point, 0 lines, 0 faces and 0 rooms. Its a dot.
In 1 dimension we have again 2 points, 1 line, 0 faces and 0 rooms. Its a line.
In 2 dimensions we have now 4 points, 4 lines, 1 face and 0 rooms. Its a square.
In 3 dimensions we have 8 points, 12 lines, 6 faces and 1 room. Its a cube.
There is one thing to be known: In order to get from one dimension to the next, the existing form is doubled and the points, which were the same, are connected.
With A points, B lines, C faces and D rooms the next would be 2 * A points, A + 2 * B lines, B + 2 * C faces and C + 2 * D rooms.
So in 4 dimensions it would be: 16 points, 32 lines, 24 faces, 8 rooms and 1 ??? (body of the fourth dimension).