I built the Hexastix 7 years ago and set it on a high shelf as decoration. Turns out the rubber bands snap after a few years due to aging... Gave me a good scare in the middle of the night! On a side note, I still haven't run out of the 72 pencils, which is a lifetime supply!
I did the exact same thing, I swapped out the rubber bands with hair ties, the rubber will also break for those after a while, but the thread covering keeps them together
Mine sat on top of the hutch above my desk in my office. The first few disintegrated while I wasn’t there, and I couldn’t see the few that had dropped out because of the decorative lip that went around the top. I didn’t realize the state it was in until I replaced the desk and tried to pick it up. It collapsed under my hands and pencils went everywhere.
Hey Matt, please consider 3d printing end caps for each face. This will help the sculpture stay in place instead of rubber bands which will degrade over time
One thing I think is pretty neat is that this is a great example of crystalline packing of alloy materials. If you assume that each kind of pencil is a discrete material that packs nicely into a crystal, the introduction of "impurities" creates an unstable, twisted mess, but with enough impurities, you eventually are able to establish a strong lattice that meshes nicely with itself
You mentioned the cylindrical packing, but I thought it was worth mentioning that both the hexagonal and the square structures are projections of a Face-Centered Cubic lattice. This also helped me to visualize how the two parts merge in the final structure. The square arrangement point to the sides of a cube, and the hexagonal arrangement point to the corners of a cube.
You know what? I'm glad I went into the comments early in the video (I'm at 4:30, just as he built the separate hexagonal and square bits); now I can watch the construction with this in mind for reference!!
The trick engineers do is they guess, they roughly calculate with like one significant digit, and sometimes that's enough to tell them the idea isn't even close to working without having to do anything precisely
True story, I was writing code all day TODAY to interact with Daniel Pikers 'Kangaroo' physics engine in Rhino3d. I love it when my nerd spaces interact this way. Daniel is an absolute legend. I've even got some custom written circle packing code from him in the recent past. Thanks for another cool video Matt.
i mean if your clothes are hexagonal and square rods and your suitcase is the shape of a regular 3D lattice of said rods you have saved a lot of time actually.
You should do another batch of pencils, the speed they sold out suggests they would be quite popular and a larger batch would allow a cheaper per unit cost, which would probably sell even better (plus, I want a set lol)
This is funny. I must have loaded up the video right when the name changed, because the title in my browser tab is "How to build a Complexastix in 67 easy steps - TH-cam", but the title below the video is "New 7-direction pencil model!"
Man, seeing this video popping up on my feed triggered forgotten memories of 7th-grade me spending all evening making the hexastix after watching that og video and posting it on my insta thinking it was the coolest thing ever. Get to relive that joy all over again lol. Thank you for all your content over these years on your channel and Numberphile. Keep up the good work!
I will never stop cracking whenever a youtuber says "as per a video of mine from a few years ago" and the embedded take is from back when he still had hair.
This reminds me a lot of a game/toy I had as a kid. It was called Kerplunk and involved creating a mesh of thin colored sticks through a tall cylinder, then placing marble on top of the sticks. From there, gameplay went a lot like Jenga, with each player removing a stick without dislodging any marbles.
I had that too. They're still making it, but they've rightly changed it to make it safer - on mine all the sticks were basically razor sharp plastic skewers.
On one hand, I've love to see this set in resin and then sliced thinly, and on the other hand I like the object exactly as it is and love the idea of being able to hold and feel it. And on the third hand, both are possible with a little more building!
What I really want to see is someone doing this with pencils that have colored wood, then embedding it in resin, then running it over a jointer and cutting away a tiny cross-section to make a video. Basically a real life version of the animation.
Rotating the plane might be interesting. The current animation is translating a plane through the 3d construct which lead me to wonder what a rotation would look like.
I usually comment small criticisms of even videos that I like. This channel is so good though. Seriously. There is no fill. Every video, and every minute of every video is high quality and entertaining.
Hey Matt! I recommend replacing the rubber bands with silicone bands. They will last a lot longer. Rubber degrades pretty quickly, especially under tension. Or you could also go with EPDM rubber bands, which are made for staying outdoors. But you can only get those in black.
Great video. Couple of pro tips: If you want the physical model to last longer replace the rubber bands with Viton or EPDM o-rings. Natural rubber bands break down over time (though are much more elastic than Viton/EPDM), but wont degrade. Buna-n or-rings (the normal rubber for o-rings) also breaks down due to ozone in the atmosphere. Secondly, with complex 3D models like this, ask if you can get a second version using a parallel view. In parallel, if you were looking at a set of rectangular boxes infinitely long face on they would just be squares on the screen. I suspect that would have been a lot easier to see where the object placement was as you can do the perspective correction in your head. For reference, the view you have is the perspective view which does match the real world a lot better, but harder to visualize long things.
Surely if he has the actual 3D model (which seems to be the case) he could just configure the viewer to display the parallel view instead of the perspective view, since the data inside the model file is a description of the true 3D state rather than just a specific 2D projection of it
@@bosstowndynamics5488It depends. If he was given a model and that is a viewer that can display whatever the input is then there would likely be viewer configurations he has access to, but if the person he was working with generated the viewer (think PDF with 3D view window) then the view type might be something controlled by the other person.
@@seeigecannon Fair enough, although that's a pretty strange way to share a model with someone who's a mathematician and hobby programmer. For what it's worth, there's a link to download the model file in the description
Fantastic video, Matt! Could there be a slight mix-up between the invariant rod packings, does the model combine hemistix and hexastix (+Π and Γ), and not tetrastix and hexastix (Π* and Γ) as mentioned? It's extremely satisfying to see how you've expanded the design so each axis represents the different rod shapes. Amazing work as always!
Nice. Daniel Piker is an under-celebrated genius. I mangled one of his early Grasshopper definitions and used it in a zoetrope project. Perfect combination of Phi distribution around a Fermat spiral, and a perfect example of how nature always beats me to the punch lol..
You might want to take a look into the crystallography of rod packings. Some structures such as garnet or the beta modification of the element manganese can be described by this kind of geometry.
Every time you do the future Matt bit I just marvel at the skill and set up that must have taken. Both you and cameraman Alex are amazing at making these videos.
FWIW if you want this sculpture to exist beyond a couple of years (due to rubber bands perishing) use elasticated hair bands instead (the ones without the metal joiners, obv). You may need to pre-stretch them a bit before use here, but they'll last far longer IME, so used ones are often ideal
Ahhh Daniel Piker, one of my favourite Grasshopper enthusiasts. What a brilliant person! I love his work. I'm so going to try and reproduce this model in Grasshopper!
The square configuration for one angle (RBG) and hexagonal configuration for another (CMYK) also has a direct geometric relationship to the Rhombic Dodecahedron's stacking patterns! If you were to cut the ends off that final combined 3D configuration, at angles symmetrically *between* the natural faces caused by the ends of the pencils, that's the polyhedron you would get. Easier to do using software than physically. Just angle a Rhombic Dodecahedron at the center, such that its hexagonal profiles line up with the CMYK faces and the square profiles will naturally line up with the RBG faces.
I would be really cool to see what the planes looks like when you go through the pencil figuration inch by inch while simultaneously rotating the entire figurations. Would make an interesting gif
picks up 7 way pencil the pencil : d̸̢̡̢̡̛͉͇̳̠̳̖̗̪̻̱̯̫̯̝̘̲̠͚̙̫̯̩̹̱͎͍̮͎͕̹̾̀̓̈͋́̏͂̊͌̽͌͊̀͑̏̇̉̓̾̋͆̾̋̎̾͋͒͐̿͌̍̍̂̔̑̐͑̍͒̋̚̚͝͝͝͠͠ọ̸̤̪͙͔͈̳̹̳̺͕̝̩̹̳͙̩̞̙̟͓̑̓̈͗͛̀̈́̆͒̅̾̂͒̈́͊̀̇͐̔́͗͐̑̾̔̉̆͌͆̔͗̒͂̓̏͂͋̕̕̚͘͜͠ͅ ̴̲̱͎͉͎̼̞̪̺̗̟̬̞̩́̓͛̌̈́̌͆̏̈͋̌̆̂͑̂͂͋͌͗̍͘̕̕͠n̸̨̢̢̻̜̪͇̟̞͎̤̩̜̘̞͉̼̦͎̫̼͉̼̖͕͉͎͔̰͎͇̣͍̲̰̫̮͔̮̯̼̤͈͎̋̉̉͂̾͂̓̀̉̈́̐̉̓̓͊̈̔̅̑̇̽̿̋̀̓͋̂̄̈́͐͘͘̚͜͠͠͝͝ͅo̶̡̩̭̫͕̝̠̩̪̱͖͎̣̼̬̺̘͚͖̯̤̤̿́̓̍̈̒̀́͒̇͌͊̈́̈̾̐͑̓̈͂̏̀̕͜ţ̴̢̛̙̻̟̬͉̙̺̘͚̬͗͐̃̅̏͆͗̋̈́̆͋̃̈́͆̓̎̔́͆́̾̒͋̄͒̒̓́͒̏̐̈͋̈́̍̀̓́̀͗̌̀̕̕͠͠ ̷̨̡͚̗̪̰̺̝̞̬͙͎̞̹̘̫͙͔̱̘͉͖̗͈̫̝̟̳̟͋͋̈͜͜͝b̶̭̙̻̰̳̘̜̥̯͓͕̳̫̝̜̳̏̓̑̚͜ͅͅë̸̡̢̧͚̻̺̤͚̤̗̺̟̲̯̮̯̦̯͍̰͕͇̤͉͍͚̮̱̝̙͈͉̟̟͇̳͈̼̠̅̂͜ ̶̡̧̧̢̡̢̧̛̛̥̲̦̹̜̱̦̰̮͍͕͔̘͖̰̜̖̘̹̞̱̜͙̹͔̝̩̪̙̖̬͉̫̘̦̺̯̀̄̅̓͗͊̓͌̍̿̔̆̇̈̈́̿͆͛͛̓̆̊͊̎̎͆͋̾̈́́͒̐̋͋̒͋͂̍͂̎̂͂͆͗̚̚̕͜͜͜͜͝a̷̢̛̛̛̦͎͙̤̐͊̈́̒͆̽̅̐̿̅̑̽̐͋̿̉̾͑́̂͊̈̅̏̕̚̚͝͝͝f̸̡̨̢̡̛͖̠̳̜̤̯̘̲̲̙̞̣̰̖̻͈̬̠̹̖̭̳̰͓͓̘͕̲͓̣͔̙̩̱̣̘̟̫̲̲̘̥̞̟̩̍̀̍͌̋̂̌̎̈̆͆́̒̀̋̃̀̚͝r̷̢̡̨̡̡̲͖͇̫̪̜̳̞͕͈̤͚͙͕̹͓̼̙̯̦̺̜̫̬̜̳̹̪̬̻̜̝̦͌̀͂̄̾͋͛a̴̢̧̡̢̨̢̢̛̯̮̹͇̟̻͓̘̲̹͕̩̙͓̫̻͔̟̥͓̹̟̻̹̭͕͇͙̲͉͕̞͎̫͓͉͖̾̐̎͊͆͐͐̇̽̀̈̅͆̌̍̈́̍͑͝͠ͅĩ̸̢̢̡̨̛̛̻̼̻̞̹̯͓̖̞̠̘̭͇͍͇̥̟̥̠͇͖̠̤̼̲̠̳͚̀͐̌̈͌̾̊̔͂̂̅̂̓͐͋̃͆̍́̾͐̋͒̓̀̔̍̄̍̏̀͛̍̕͘͝͝͝͠͝ͅͅḍ̷̲͙͙̞̱̘̜̖̼̝͔̺̩͇̯̲͕̬̯̒͗͐͋̍́̏͊̊̇̓͊̑̏̎̈́̾́͗̏͠ͅ
I'd like to see this with dodecagonal pencils. That would work with the square and hexagonal lattices making the pattern more perplexing for the casual observer.
For a true exercise in understanding 2D to 3D, deciphering that gif, and duplicate the 3D model, could be a big brain moment. We humans even understand what a 3D object is, and to do that is still a challenge, let alone what a 2D lifeform would have to do, to comprehend it. Makes me wonder how far off we are in understanding what a 4D object actually is, compared to an entity that does know.
Should stamp the Parker Square numbers on the ends of the square one :D - always push for brand recognition ~.^ Thank you to everyone who was involved in making this video, I enjoyed it a lot.
0:09 Well… it’s a tessellation, so the starting point is more finite than it seems; but I think you’d start with various points, decide their vectors and then determine how their movement can be “swelled”, so their movement is so tactile (or tangential, if you like; but maybe there’s a better word) which would then shape the polygons we see Testing may be necessary to establish points that don’t actually simply eradicate each other, but maybe even this design include a few additional points that were eradicated, leaving this successful lot 💙
now that was a clever video trick: usually, youtubers just insert video clips of "future me", explaining something later. but this one? basically talking with your future self in a blended shot. funny trick. nothing fancy, but a good way to repurpose it.
Suppose that, instead of groups of distinct pencils, this shape were built out of intersection square and hexagonal prisms. What does the volume in which they intersect look like?
@StandUpMaths Dixon makes a triangular pencil. The aptly named "Triconderoga". A play on the name of their popular "Ticonderoga" pencil. They are fairly large at the widest part.(It looks like a regular sized pencil that has a little extra added to make it triangular.) But the shape makes them very easy to hold. The cross section looks similar to the triangle version of a shape with constant width.
I've never seen a strictly triangular pencil but Reuleaux triangle-like cross-sections seem somewhat common for presumably ergonomical reasons, although in my view a regular hexagonal pencil offers much of the same benefits. Come to think of it, that's probably why you don't see square pencils, must be really awkward to hold.
If you'd record "future matt" first and leave the structure on the table, then you could have picked it up when filming "past matt" after. Could be a fun trick to do in a future video.
i wasnt really sure what you meant by "section of the lattice" but when you started putting in more pencils to make squares and hexagons it made a lot of sense
You should 3d print holders for the pencils, then you wouldn’t need rubber bands and you could have models of each color externally of the final model which could be fun to have
I wouldn't call that set expensive, it's quite less than a dollar for each pen, which is customised to have a nice vibrant colour and, most importantly, "ORTHOGONAL Z-AXIS".
I thought he would have by now figured out to simply laser cut a template for each color. Stick the right color sticks in the right holes in the template, and then satisfaction when they all slide together. You just need two friends to help.
Hey Matt, Great video, but since they have sold out, can you put that in the description in place of the link please? They sold out in a day, and that is a shame for me lol. Thanks.
That you can go and order geometrically suitable penciles to build physical models of CGI mathematical marvels is just downright wonderful. That you can do so and share it with the world also marvellous.
I built the Hexastix 7 years ago and set it on a high shelf as decoration. Turns out the rubber bands snap after a few years due to aging... Gave me a good scare in the middle of the night! On a side note, I still haven't run out of the 72 pencils, which is a lifetime supply!
I did the exact same thing, I swapped out the rubber bands with hair ties, the rubber will also break for those after a while, but the thread covering keeps them together
so glad I glued mine together😂
Mine are back in a coffee can for the same reason, every few months, I hear them calling 😂
Mine sat on top of the hutch above my desk in my office. The first few disintegrated while I wasn’t there, and I couldn’t see the few that had dropped out because of the decorative lip that went around the top. I didn’t realize the state it was in until I replaced the desk and tried to pick it up. It collapsed under my hands and pencils went everywhere.
Yes those rubber bands self destruct after "a time". &sually by melting and messing everyrhing they were touching.
Love it when Matt interacts with future Matt.
it's very telling that you didn't call him "past matt"
I'm sure the camera person also loves working with them. Maybe we should get Matt a really long scarf and a sonic screwdriver.
We got Past Matt in this video too! We got all the Matts!
@@omatic_opulis9876 nope. As a rule, Past Matt has hair.
Now let's talk about the real shape of the Earth.
the next step is to submerge it in epoxy and cut it
I second this motion!
And then stop motion animation layer by layer
I third this motion
My thoughts exactly!
I fourth this motion!
I very much appreciate the CMYK/RGB groupings. Very satisfying.
The magenta ones were annoyingly red though.
@@pepebriguglio6125yes, they looked very red on my screen as well. I wonder if they look more magenta in real life.
@@pepebriguglio6125 Some of that may well be the camera.
@@Scoots1994
I think so too. And definitely hope so.
7:45 "I'm going to keep both of these, because I like them."
Never change Matt Parker.
Hey Matt, please consider 3d printing end caps for each face.
This will help the sculpture stay in place instead of rubber bands which will degrade over time
I just uploaded a 3d printable gyroid holder for these pencils - can't post a link here, but search my name on Mathstodon and you'll find it
One thing I think is pretty neat is that this is a great example of crystalline packing of alloy materials.
If you assume that each kind of pencil is a discrete material that packs nicely into a crystal, the introduction of "impurities" creates an unstable, twisted mess, but with enough impurities, you eventually are able to establish a strong lattice that meshes nicely with itself
woaah
I admire that he has the Parker Square hanging on his wall.
I want to believe that Brady framed it and gave it to him as a gift.
@@pancakelegendThat does very much sound like a Brady thing to do
@@pancakelegend well, that was correct, lol
2:13 putting back the black pencil in the yellows' box
Watching that brought sweat to my forehead
My eyebrow twitched 😂
Nice! Now we just need a soccer ball based on this 14-sided figure.
That would basically be a cuboctahedron.
@@ObiWahn68aka a folded up Rubik's snake.
It could also be a truncated cube or octahedron depending on weighting @ObiWahn68
....ok, yes. Someone show @jonpaulsballs
1:30 sometimes I think Matt shaved his head only to be able to make "my hair fell out" jokes for all eternity! haha
He looks so good bald tho
You mentioned the cylindrical packing, but I thought it was worth mentioning that both the hexagonal and the square structures are projections of a Face-Centered Cubic lattice. This also helped me to visualize how the two parts merge in the final structure. The square arrangement point to the sides of a cube, and the hexagonal arrangement point to the corners of a cube.
I had one of those "ohhhhhhhhhh, huh, neat!" Moments when I read this
You know what? I'm glad I went into the comments early in the video (I'm at 4:30, just as he built the separate hexagonal and square bits); now I can watch the construction with this in mind for reference!!
“I now need to guess. Not guess. Very carefully calculate”-everyone at their jobs everyday 😂
Or if we're feeling slightly more honest, "estimate"
why you gotta call me out like that
That's what mathematics is all about, one you get to a sufficiently advanced level.
The trick engineers do is they guess, they roughly calculate with like one significant digit, and sometimes that's enough to tell them the idea isn't even close to working without having to do anything precisely
At first I thought "wow I bet that's not what the pencil manufacturer thought they'd be used for" but you know what? no. this *is* art.
I think the manufacturer realized some shenanigans were gonna happen, just purely from the choices of label and color for each box of pencils.
Surprised the manufacturer didn't get a shout out
As someone who's studied graphic design, I love your choice of colours for the pencils.
Yep. Big fan of the additive & subtractive color choices.
RGB and CMYK!!
In that meaning, a Complexastix is what happens when you put a real Hexastix with an imaginary Hexastix together.
a parkerstix.
How do you maintain orthogonality?
Yo
Head canon that, while Matt comes in present, future, and editing varieties, camera person Alex is eternal
And the only thing worse than getting a regular cameraman angry is making an eternal cameraman angry
Not eternal. Timeless. He experiences every moment from his birth to his death simultaneously.
This video also featured Past Matt, a rare treat!
@@blaz2892 Oh god he's a photon
True story, I was writing code all day TODAY to interact with Daniel Pikers 'Kangaroo' physics engine in Rhino3d. I love it when my nerd spaces interact this way. Daniel is an absolute legend. I've even got some custom written circle packing code from him in the recent past. Thanks for another cool video Matt.
Instead of packing, I watched this. Worth it.
instead of packing yourself, you watched someone else pack instead?
Technically, this is a sort of packing.
i mean if your clothes are hexagonal and square rods and your suitcase is the shape of a regular 3D lattice of said rods you have saved a lot of time actually.
@@CjqNslXUcM That's a vid I'd like to see, lol
You should do another batch of pencils, the speed they sold out suggests they would be quite popular and a larger batch would allow a cheaper per unit cost, which would probably sell even better (plus, I want a set lol)
17:40 Mr. Parker appears to slide the entire pencil directly up his nose.
This is funny. I must have loaded up the video right when the name changed, because the title in my browser tab is "How to build a Complexastix in 67 easy steps - TH-cam", but the title below the video is "New 7-direction pencil model!"
Man, seeing this video popping up on my feed triggered forgotten memories of 7th-grade me spending all evening making the hexastix after watching that og video and posting it on my insta thinking it was the coolest thing ever. Get to relive that joy all over again lol. Thank you for all your content over these years on your channel and Numberphile. Keep up the good work!
I will never stop cracking whenever a youtuber says "as per a video of mine from a few years ago" and the embedded take is from back when he still had hair.
Crystallography finally getting its time to shine in maths science communication :')
wanted this so bad but they're already sold out and it's only been 2 hours, i hope these are available for purchase again someday
This reminds me a lot of a game/toy I had as a kid. It was called Kerplunk and involved creating a mesh of thin colored sticks through a tall cylinder, then placing marble on top of the sticks. From there, gameplay went a lot like Jenga, with each player removing a stick without dislodging any marbles.
I had that too. They're still making it, but they've rightly changed it to make it safer - on mine all the sticks were basically razor sharp plastic skewers.
@@manjackson2772 yep. Kids had so many great and dangerous toys back then. Lawn darts come to mind.
On one hand, I've love to see this set in resin and then sliced thinly, and on the other hand I like the object exactly as it is and love the idea of being able to hold and feel it. And on the third hand, both are possible with a little more building!
What I really want to see is someone doing this with pencils that have colored wood, then embedding it in resin, then running it over a jointer and cutting away a tiny cross-section to make a video. Basically a real life version of the animation.
Well, not pencils at that point, just solid rods of different colored wood.
Thank you for this Parker-Piker collaboration
Or Piker-Parker? Either way, I sense naming opportunities...
Piker is the Parker Parker. What matters is that he had a go, and is mostly correct.
At least they didn't pick a peck of pickled peppers
Rotating the plane might be interesting. The current animation is translating a plane through the 3d construct which lead me to wonder what a rotation would look like.
The 3D modeling is impressive. Good work Daniel!
Nice bonus that 67 is prime too. The 19th prime, which is again prime. 🙂
I usually comment small criticisms of even videos that I like.
This channel is so good though. Seriously. There is no fill. Every video, and every minute of every video is high quality and entertaining.
Hey Matt! I recommend replacing the rubber bands with silicone bands. They will last a lot longer. Rubber degrades pretty quickly, especially under tension. Or you could also go with EPDM rubber bands, which are made for staying outdoors. But you can only get those in black.
Next step: cast in resin, then slice to make a real instance of the original animation!
Alternatively, you could 3d print the model and film a time lapse of it.
Alright then.... post this on TH-cam when you're done please 🙏
@estherstreet4582 don't tempt me 😅
Great video. Couple of pro tips:
If you want the physical model to last longer replace the rubber bands with Viton or EPDM o-rings. Natural rubber bands break down over time (though are much more elastic than Viton/EPDM), but wont degrade. Buna-n or-rings (the normal rubber for o-rings) also breaks down due to ozone in the atmosphere.
Secondly, with complex 3D models like this, ask if you can get a second version using a parallel view. In parallel, if you were looking at a set of rectangular boxes infinitely long face on they would just be squares on the screen. I suspect that would have been a lot easier to see where the object placement was as you can do the perspective correction in your head. For reference, the view you have is the perspective view which does match the real world a lot better, but harder to visualize long things.
Surely if he has the actual 3D model (which seems to be the case) he could just configure the viewer to display the parallel view instead of the perspective view, since the data inside the model file is a description of the true 3D state rather than just a specific 2D projection of it
@@bosstowndynamics5488It depends. If he was given a model and that is a viewer that can display whatever the input is then there would likely be viewer configurations he has access to, but if the person he was working with generated the viewer (think PDF with 3D view window) then the view type might be something controlled by the other person.
@@seeigecannon Fair enough, although that's a pretty strange way to share a model with someone who's a mathematician and hobby programmer. For what it's worth, there's a link to download the model file in the description
@@bosstowndynamics5488 oh nice. Thanks. I didn't even think to check that.
@@seeigecannon To be fair, neither did I at first
Fantastic video, Matt! Could there be a slight mix-up between the invariant rod packings, does the model combine hemistix and hexastix (+Π and Γ), and not tetrastix and hexastix (Π* and Γ) as mentioned? It's extremely satisfying to see how you've expanded the design so each axis represents the different rod shapes. Amazing work as always!
Glad to see that you’re getting enough enrichment in your enclosure
Nice. Daniel Piker is an under-celebrated genius. I mangled one of his early Grasshopper definitions and used it in a zoetrope project. Perfect combination of Phi distribution around a Fermat spiral, and a perfect example of how nature always beats me to the punch lol..
You might want to take a look into the crystallography of rod packings. Some structures such as garnet or the beta modification of the element manganese can be described by this kind of geometry.
Every time you do the future Matt bit I just marvel at the skill and set up that must have taken.
Both you and cameraman Alex are amazing at making these videos.
Thank you for making these concepts understandable for those who don't study maths.
I have to applaud the dedication to your particular brand of crazy. It's great stuff, keep it up.
FWIW if you want this sculpture to exist beyond a couple of years (due to rubber bands perishing) use elasticated hair bands instead (the ones without the metal joiners, obv). You may need to pre-stretch them a bit before use here, but they'll last far longer IME, so used ones are often ideal
21:38
"the square cross-sections are once again square with the square. Those squares are square square.
...
Which apparently is hip."
🎶It's not too hard to figure out🎶
The Hexastix you taught me how to make is still on the shelf. And I've still not run out of the leftover pencils
No plug for the custom pencil manufacturer? They did a cracking job at producing very nice pencils!
I like how the cuboid sticks are RGB and the hexagonal prism sticks are CYMK
at 1:42 I thought he was going to say "wouldn't it be great if I still had my hair"
Ahhh Daniel Piker, one of my favourite Grasshopper enthusiasts. What a brilliant person! I love his work. I'm so going to try and reproduce this model in Grasshopper!
Would be cool to build that but with pencils of carefully calculated specific lengths so that the result has a spherical overall shape.
The square configuration for one angle (RBG) and hexagonal configuration for another (CMYK) also has a direct geometric relationship to the Rhombic Dodecahedron's stacking patterns!
If you were to cut the ends off that final combined 3D configuration, at angles symmetrically *between* the natural faces caused by the ends of the pencils, that's the polyhedron you would get. Easier to do using software than physically. Just angle a Rhombic Dodecahedron at the center, such that its hexagonal profiles line up with the CMYK faces and the square profiles will naturally line up with the RBG faces.
I like that people are still using the 3b1b puzzle mugs so long after that video came out.
I've had a rough day and a Matt Parker video is exactly what I needed.
"Hip to be square" -- I got that reference.
I imagine this gif represents how busy crossroads will look like in some near (or not so near) future
I would be really cool to see what the planes looks like when you go through the pencil figuration inch by inch while simultaneously rotating the entire figurations. Would make an interesting gif
Every triangle is a love triangle, if you love triangles! But with that Love Triangle, you can rediscover and express your love for triangles :D
Not gonna lie: that’s a pretty cool sculpture. 👏
I enjoyed this video a lot. I love the fun and creative Matt Parker, Both the past, future and now versions of him.
11:54 “Coming in with their ‘hexagonalness…’” Hexes are truly the bourgeoisie of polygons, aren’t they!
picks up 7 way pencil
the pencil : d̸̢̡̢̡̛͉͇̳̠̳̖̗̪̻̱̯̫̯̝̘̲̠͚̙̫̯̩̹̱͎͍̮͎͕̹̾̀̓̈͋́̏͂̊͌̽͌͊̀͑̏̇̉̓̾̋͆̾̋̎̾͋͒͐̿͌̍̍̂̔̑̐͑̍͒̋̚̚͝͝͝͠͠ọ̸̤̪͙͔͈̳̹̳̺͕̝̩̹̳͙̩̞̙̟͓̑̓̈͗͛̀̈́̆͒̅̾̂͒̈́͊̀̇͐̔́͗͐̑̾̔̉̆͌͆̔͗̒͂̓̏͂͋̕̕̚͘͜͠ͅ ̴̲̱͎͉͎̼̞̪̺̗̟̬̞̩́̓͛̌̈́̌͆̏̈͋̌̆̂͑̂͂͋͌͗̍͘̕̕͠n̸̨̢̢̻̜̪͇̟̞͎̤̩̜̘̞͉̼̦͎̫̼͉̼̖͕͉͎͔̰͎͇̣͍̲̰̫̮͔̮̯̼̤͈͎̋̉̉͂̾͂̓̀̉̈́̐̉̓̓͊̈̔̅̑̇̽̿̋̀̓͋̂̄̈́͐͘͘̚͜͠͠͝͝ͅo̶̡̩̭̫͕̝̠̩̪̱͖͎̣̼̬̺̘͚͖̯̤̤̿́̓̍̈̒̀́͒̇͌͊̈́̈̾̐͑̓̈͂̏̀̕͜ţ̴̢̛̙̻̟̬͉̙̺̘͚̬͗͐̃̅̏͆͗̋̈́̆͋̃̈́͆̓̎̔́͆́̾̒͋̄͒̒̓́͒̏̐̈͋̈́̍̀̓́̀͗̌̀̕̕͠͠ ̷̨̡͚̗̪̰̺̝̞̬͙͎̞̹̘̫͙͔̱̘͉͖̗͈̫̝̟̳̟͋͋̈͜͜͝b̶̭̙̻̰̳̘̜̥̯͓͕̳̫̝̜̳̏̓̑̚͜ͅͅë̸̡̢̧͚̻̺̤͚̤̗̺̟̲̯̮̯̦̯͍̰͕͇̤͉͍͚̮̱̝̙͈͉̟̟͇̳͈̼̠̅̂͜ ̶̡̧̧̢̡̢̧̛̛̥̲̦̹̜̱̦̰̮͍͕͔̘͖̰̜̖̘̹̞̱̜͙̹͔̝̩̪̙̖̬͉̫̘̦̺̯̀̄̅̓͗͊̓͌̍̿̔̆̇̈̈́̿͆͛͛̓̆̊͊̎̎͆͋̾̈́́͒̐̋͋̒͋͂̍͂̎̂͂͆͗̚̚̕͜͜͜͜͝a̷̢̛̛̛̦͎͙̤̐͊̈́̒͆̽̅̐̿̅̑̽̐͋̿̉̾͑́̂͊̈̅̏̕̚̚͝͝͝f̸̡̨̢̡̛͖̠̳̜̤̯̘̲̲̙̞̣̰̖̻͈̬̠̹̖̭̳̰͓͓̘͕̲͓̣͔̙̩̱̣̘̟̫̲̲̘̥̞̟̩̍̀̍͌̋̂̌̎̈̆͆́̒̀̋̃̀̚͝r̷̢̡̨̡̡̲͖͇̫̪̜̳̞͕͈̤͚͙͕̹͓̼̙̯̦̺̜̫̬̜̳̹̪̬̻̜̝̦͌̀͂̄̾͋͛a̴̢̧̡̢̨̢̢̛̯̮̹͇̟̻͓̘̲̹͕̩̙͓̫̻͔̟̥͓̹̟̻̹̭͕͇͙̲͉͕̞͎̫͓͉͖̾̐̎͊͆͐͐̇̽̀̈̅͆̌̍̈́̍͑͝͠ͅĩ̸̢̢̡̨̛̛̻̼̻̞̹̯͓̖̞̠̘̭͇͍͇̥̟̥̠͇͖̠̤̼̲̠̳͚̀͐̌̈͌̾̊̔͂̂̅̂̓͐͋̃͆̍́̾͐̋͒̓̀̔̍̄̍̏̀͛̍̕͘͝͝͝͠͝ͅͅḍ̷̲͙͙̞̱̘̜̖̼̝͔̺̩͇̯̲͕̬̯̒͗͐͋̍́̏͊̊̇̓͊̑̏̎̈́̾́͗̏͠ͅ
I'd like to see this with dodecagonal pencils. That would work with the square and hexagonal lattices making the pattern more perplexing for the casual observer.
20:55 is the most parker square thing i ever heard
For a true exercise in understanding 2D to 3D, deciphering that gif, and duplicate the 3D model, could be a big brain moment. We humans even understand what a 3D object is, and to do that is still a challenge, let alone what a 2D lifeform would have to do, to comprehend it. Makes me wonder how far off we are in understanding what a 4D object actually is, compared to an entity that does know.
Is there a possibility you can order another batch of pencils and sell them? They sold out already and I bet a lot of people would like it :D
You should design a football shaped as the convex hull of a subset of this lattice
Sold out in mere hours. I'm impressed.
This is so satisfying. I love the almost regular lattices.
Should stamp the Parker Square numbers on the ends of the square one :D - always push for brand recognition ~.^ Thank you to everyone who was involved in making this video, I enjoyed it a lot.
0:09
Well… it’s a tessellation, so the starting point is more finite than it seems; but I think you’d start with various points, decide their vectors and then determine how their movement can be “swelled”, so their movement is so tactile (or tangential, if you like; but maybe there’s a better word) which would then shape the polygons we see
Testing may be necessary to establish points that don’t actually simply eradicate each other, but maybe even this design include a few additional points that were eradicated, leaving this successful lot 💙
I just about had a heart attack when you put the black pencil in the yellow pencil box.
HE PUT THE BLACK PENCIL IN THE BOX WITH YELLOW PENCILS!
now that was a clever video trick: usually, youtubers just insert video clips of "future me", explaining something later. but this one? basically talking with your future self in a blended shot. funny trick. nothing fancy, but a good way to repurpose it.
Suppose that, instead of groups of distinct pencils, this shape were built out of intersection square and hexagonal prisms. What does the volume in which they intersect look like?
@StandUpMaths Dixon makes a triangular pencil. The aptly named "Triconderoga". A play on the name of their popular "Ticonderoga" pencil. They are fairly large at the widest part.(It looks like a regular sized pencil that has a little extra added to make it triangular.) But the shape makes them very easy to hold. The cross section looks similar to the triangle version of a shape with constant width.
I've never seen a strictly triangular pencil but Reuleaux triangle-like cross-sections seem somewhat common for presumably ergonomical reasons, although in my view a regular hexagonal pencil offers much of the same benefits. Come to think of it, that's probably why you don't see square pencils, must be really awkward to hold.
You could put it in a container, fill it with clear resin and put it on a lathe to make a really cool looking structure out of it.
If you'd record "future matt" first and leave the structure on the table, then you could have picked it up when filming "past matt" after. Could be a fun trick to do in a future video.
i wasnt really sure what you meant by "section of the lattice" but when you started putting in more pencils to make squares and hexagons it made a lot of sense
i sometimes think about your hexastix, and i'm really happy you decided to make a followup/part 2
Could this work with pentagonal and hexagonal pencils to make a regulation football with the ends of the pencil?
You should 3d print holders for the pencils, then you wouldn’t need rubber bands and you could have models of each color externally of the final model which could be fun to have
I still have my Hexastix on my desk at work. I changed the rubber bands to strings because they started to break.
I wouldn't call that set expensive, it's quite less than a dollar for each pen, which is customised to have a nice vibrant colour and, most importantly, "ORTHOGONAL Z-AXIS".
I thought he would have by now figured out to simply laser cut a template for each color. Stick the right color sticks in the right holes in the template, and then satisfaction when they all slide together. You just need two friends to help.
Once I saw it was only 67 steps.. I was hooked in!
Hey Matt,
Great video, but since they have sold out, can you put that in the description in place of the link please? They sold out in a day, and that is a shame for me lol.
Thanks.
Thank you so much for putting captions on this one ily matt
ok, now glue them together and cut it to make a crossection 😀also, what pencil manufacturer makes custom ones?
The triangle pencil visualization was AMAZING. Trippy! 😂
That you can go and order geometrically suitable penciles to build physical models of CGI mathematical marvels is just downright wonderful. That you can do so and share it with the world also marvellous.
Now you need to encase it in white resin and carefully sand off millimeter by millimeter, taking photos of each slice and animate it!
"Square… which apparently is hip"
I love that song!
And 67 is a prime! What a lovely non-Parker model it is! 😍
Highly relatable, as I am currently making six color space frame models, but using members with a circular cross section.
"Alright, I'm doing them all" ...watching you descend decisively down a rabbit gole was wonderful. Matt, thanks, helps a lot!
#nosquareisasquaresquare
Subscriber Matt here, so many Matts! I love it!
Aw, I wanted to see the animated cross section of the hexasticks...
We need more pencils on Math Gear pleeeease