Ultimate Solids of Constant Width

I love to geometric objects with strange properties. Have we finally found the perfect solid of constant width?
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[@tarrute]

This dude will freak when he finds out about spheres!

[@yeleoh]

No

[@tarrute]

No to what part?

[@tarrute]

I’m confused.

[@yeleoh]

@@tarrute freak out

[@HeyHebi]

woosh?

[@andersjonsson3650]

If this is the ultimate solid of constant width, where would you place the sphere?

[@ShenHibiki]

Thanks. I decided to check the comments 'cause that was EXACTLY what was in my mind XD

[@nThanksForAllTheFish]

Sphere would be trivial solid of constant width..

[@santiagogonzalez9518]

If this is the ultimate, the sphere is clearly the first one.

[@JDSachs]

I assume by 'ultimate' they mean the max width compared to volume. If you melt one of these into a sphere, the width would be less.

[@a.schluchter2772]

In the future, you may want to refrain from asking most internet comment sections as to where you should put a spherical object

[@costerowywot]

drinking game - take a shot everytime he says "constant width"

[@lasarith2]

Thanos: forget everything in perfect Balance, a Solid of Constant width, is the new thing now .

[@FMFvideos]

perfect constant width as all things should be

[@licensetodrive9930]

Have you tried Googling the word Thanos and clicking on the glove?

[@lasarith2]

licensetodrive ye I ha

[@ikmnification5737]

That intro with the unique rolling objects would have Tim from Grand Illusions saying, "uh, what fun!".

[@h-Films]

Yah

[@excellinkus]

I drew a triquetra using the golden ratio 1:1.618... Basically an overlap between any two circles of ~0.38:1 instead of 0.5:1. The triangle in the center and the three lobes at 120° were exactly the same proportions for both ratios!

[@avejst]

Wow, and the project rolls off again😀👍 Thanks for sharing this👍😀

[@YukonK9]

You got me obsessed with solids of constant widths a few years ago. Ever since then, I can't get over with them!

[@spikekent]

Great video Angus, looking forward to more on this enthralling subject and what you do with it.

[@ollienor]

I modelled the proper one in fusion 360, the 3D object of constant width incorporating Patrick Roberts equations for the edges. I've been using Inventor for 10+ years and fusion for 2 days now. I admit, it was a challenge but I got there and it looks great! Wouldn't have done it without your video. Cheers!

[@tinkertv]

That is oddly satisfying :O

[@FusionSource]

Oh my, they are gorgeous, such beautiful symmetry and absolutely amazing. Thanks for the video.

[@g0balot]

Beautiful video. Thanks

[@OktoPutsch]

Very interesting stuff, mate, thanks for sharing !

[@RonFloyd]

Really cool Angus! Thanks.

[@cavinrauch]

That's so awesome that they contacted you !

[@WolfsHaven]

Absolutely amazing. If you can perfect the printable stl, it will be worth buying.

[@WPGinfo]

Beautiful!

[@ericswinson3719]

This man made me fall in love with these crazy shapes

[@nickp4793]

Wow, this was an interesting video. Thanks.

[@Veptis]

I love your background music, it reminds me of the early work by Rameses B-

[@lordmarshmal_0643]

The Gemcraft series has the Reuleaux Triangle as its main icon (it's actually the shape of the simplest gem/weapon in the game), so today I learned a bit about a feature of one of my favorite games!

[@biglwrab9634]

Thank you for making me get a 3D printer, it was worth it!

[@TheMonyarm]

I need some dice based on these shapes.

[@brendanh6361]

*and some say he is still rolling to this day*

[@zero_gravity5861]

It would only work if it had a weight in a cavity shaped like the dual of the shape

[@_moffett]

Thanks I’m staying awake all night now. damn you (not really)

[@Jellylamps]

Now i wanna see other solids of constant width based off of the other platonic solids

[@andyphipps01]

Hi Angus - Great channel and love your reviews! I was wondering what you would recommend for a high res hobby 3d printer for miniatures. I was thinking resin (work in research so know handling toxic chemicals), but not sure on what model for a hobby in 2019?

[@efnick96]

I really like the production of this video. Keep it up. I have a non related question: Thoughts on the Artillery (Evnovo) Sidewinder x1? Even if you haven't test it, I just want you thoughts. :) Thanks

[@beeblaine539]

I successfully did this a couple years ago in fusion with a very complex surface loft to get that spherical envelope for the corner, revolving doesn’t work becouse it’s around a curved axis

[@ChrstphreCampbell]

could your replace your tires with them ?

[@djslothario]

I don't know if you're serious or not, but car tires wouldn't work because you want a reasonable and even contact area with the road -- these would slip. You could build a tricycle or some other vehicle that isn't capable of killing someone with them, though!

[@h-Films]

yiou would bavebyahey

[@xaytana]

So, after some work, I've figured out how to model these, and it's so stupidly easy. And it's only six extra steps after making the Reuleaux Tetrahedron. It only requires a variable radius fillet.

[@Acoustic-Rabbit-Hole]

I see the sound of this shape as an F-sharp. And a full, sort of grass-green in color. I also know that 360 hertz is a basic F-sharp note. Meaning that this shape is three sides that each are the curve of a sphere. And just like a sphere, the shape rolls evenly. Therefore this shape is a solid manifestation of The Divine, because a zero (circle) is equivalent to Nothing. This solid-of-constant-width is, therefore, magical.

[@dorjedriftwood2731]

Wow downright spiritual

[@INeed333Quid]

instead of using spheres on the corners have you tried using spherical pipes on the edges? sorry if this is a red herring aha, i'm trying to imagine and in my brain at least that seems to work

[@craiggee5370]

I'm wondering if you could do a 3D scan of those and then print them out.

[@kly8105]

Thumbnail: "perfection at last" Me: ohhh so that's what the gamesphere 2 will look like.

[@NathanKraemer]

Just backed the Kickstarter for a steel one : $28 plus $5 shipping Total sucker compliant mechanisms and cool shapes.

[@reneetaylor7596]

Hi, would you be able to do a review of the CoLiDo DIY 3D printer?

[@cosmicjenny4508]

0:54 The UK and all of “the territories” in the British Isles (Isle of Man, Gibraltar etc.) have that shape of coin. We also have a 20 Pence piece that has the same property, and I’m pretty sure they were the first seven-sided coins, ever.

[@Meblin74]

Angus it's a 50 pence piece not Cent The 50 Cent piece is just a round gold coin

[@xaytana]

Could you do the sphere sweep to any platonic solid for the same effect?

[@hadinossanosam4459]

The problem with that would be the center of the spheres... the tetrahedron is unique among platonic solids in that it has a corner opposed to a face, instead of another face (which is also why it makes for a weird dice)... You might be able to make it work, but I suspect it wouldn't look as symmetrical.

[@dsscse]

I nearly fell off my stool when I saw the ERIE 50p 30yrs since I spent one. Oh since you are into interesting solids order yourself a Gomboc, a mono-monostatic body that is the most sphere-like body, apart from the sphere itself. My wife and I bought each other one for our birthdays in 2007. Just a year after they were physically produced , until 2006 they were just a mathematical equation ! FYI Great series of vids.

[@jamespowell7231]

I feel you. I often feel like a strange geometric object. 🤣

[@PRO3DESIGN]

I love your passion. I can only strive to make similar good content. However I am more a DIY channel

[@soaringred882]

Fun party game: take a shot everytime he says solid(s) of constant width

[@kupfeli]

Have you been able to construct a good Meissner Tetrahedron in Fusion 360? If not, I believe I might have done it, only using lofts, no spheres at all, also no 2D spheres.

[@yourdesign3dprinting414]

Does it required support material to print?

[@Blamm83]

I did a drinking game on every "solid of constant width" and can't feel my legs anymore now

[@bukscoetzer]

@Angus instead of using spheres in the corners rather use variable Radii fillet where the peaks have a almost zero radius and the mid sections have your max sphere radius. PM me if you need more explanation.

[@aokimika9249]

Ok. I want one it those.

[@AmaroqStarwind]

Use these as bearings!

[@wuerfelschmied6906]

I think I need to make a d4 of constant width.

[@MakersMuse]

You would need a pretty tough surface to roll these bad boys! Would work pretty good though.

[@wuerfel_schmied]

@@MakersMuse yeah I like to use leather lined trays or dice towers for this.

[@amoose136]

How about a unique surface that allows a standard D6 to roll like a sphere.

[@wuerfelschmied6906]

@@amoose136 tricky, but maybe doable. In 2d its no problem. But how would you read your dice ^^

[@jenniferwhitewolf3784]

The 'un-ball' bearing

[@LiLi-or2gm]

Oh, it's a spheramid (and definitely not a shining trapezohedron)!

[@twinklestar3556]

This was a tasty video! What would be a better way to say that?❤

[@FMFvideos]

You can't test if a surface is even with 3 base points. Needs at least 4. 3 legs under the plane may give a false impression of planar while keeping all legs in contact

[@spiplayz6503]

Yay

[@maximthemagnificent]

For complex and precise shapes I still just write some code to spit out an obj file. I should probably learn OpenSCAD at some point...

[@bobmvideos]

I wrote an openscad script to show this construction a while back www.thingiverse.com/thing:2323357

[@Birb_of_Judge]

I need help. I am looking for s good 3D printing Surface with the size of 310mmx310mm-330mm330mm

[@RomanoPRODUCTION]

Ultimate sexiness like Angus

[@jimtotten5928]

Is this not a Meissner Tetrahedron? Are all 6 edges of the Reuleaux Tetrahedron modified here?

[@firearmsstudent]

Final video about solids of constant width... to be continued.

[@niknah]

Here's one that's already finished. www.kickstarter.com/projects/ghrostyschuff/roloids-solids-of-constant-width/updates

[@Chrissssssssssssssssssss]

*Watch this on x2 its better!*

[@aveoxus1139]

A solid of constant width, not to be confused with the solid of constant girth. Also known as Big Chungus

[@z4zuse]

Maybe easier to define in OpenSCAD?

[@davidwillmore]

I would like to take a swing at that.

[@TroyMackay]

Was going to give it a crack, but a quick google saved me the time: ceptimus.co.uk/?p=345

[@TroyMackay]

Couldn't resist: www.thingiverse.com/thing:3620748 - combines the fairly efficient code of ceptimus with the symmetry of xtalgrafix

[@bobmvideos]

@@TroyMackay I think you might have too much symmetry. According to that reference "Note that only three of the edges are rounded"

[@TroyMackay]

@@bobmvideos In the original ceptimus code, yes. Not in the xtalgrafix maths I implemented on top.

[@aeislugh]

I wonder how these would work as a 4 sided die

[@21gioni]

Ursinos it is called a ball 🎱 because it can not be done with a cube shape. Solids of constant width do not work with a cube. There is a way each side must have a depression in the center. Essentially you have a ball with six depressions. What I found interesting is certain geometric shapes can not be turned into Solids of constant width. But it is fun experimenting with different shapes. You must always begin with a sphere.

[@spacenoodles5570]

Wait, a reuleaux tetrahedron is not a solid of constant width‽ why?

[@CuulX]

Wikipedia has the answer I believe. I didn't check the proof yet so can't explain it to you myself.

[@StephenBoyd21]

How about a solid of constantly variable width.

[@samuelschwager]

Backed :)

[@Krasinski1]

I want a meissner tetrahedron... can't find any

[@remchaill9898]

Surely the "ultimate solid of constant width" would have to be the sphere? What is the definition of "solid of constant width" that excludes the sphere?

[@pablodv87]

A sphere is a particular case of a solid of constant width, that also has constant radius.

[@normoloid]

These weird shapes could become even weirder if they would have half water and half oil in them, and holes in every "cell" in them to create a sort of perpetual imbalance in liquid form inside of an imbalanced shape.

[@programmingmaster03]

Mmmm rotary engine!

[@Crazyoldman84]

Can you make an antweight combat robot please.

[@F2_CPB]

Your interest is kind of interesting

[@maddoxflores2555]

can we get angus 2 half a million?

[@Stojce_]

Dorito Jesus

[@darren990]

that's to much super girl for me lol. nice vid

[@tenlittleindians]

A nice try but your being held back by your software. FreeCad open source and has great people willing to help out with problems such as this. Here's a link to how to design this in FreeCad: kzbin.info/www/bejne/norIh3Sjrtpqhdk Please subscribe to his channel and throw out a thank you for taking on your problem after I suggested it in a comment in another of his great FreeCad tutorials.

[@wastedangelematis]

constant THICC !!!!

[@klakshmivaraprasadarao2935]

Hi bro

[@DoctorJ3kyll]

Think twice before you back this on kickstarter and do some homework.

[@gilshtrahman8696]

1:00 kinda also looks like an israeli 5₪(shekel) coin

[@neopada9091]

What is this witchcraft? It's not a ball how does it work?

[@gilshtrahman8696]

please PLEASE build a 3d printed wankel rotary engine that would be so cool🤤

[@leif1075]

But a riuleaux triangle is a three dimensional example of an object of constant width..

[@sab611]

Hi there. It's called a Meissner Tetrahedron. I made a nice clean version of it in Fusion 360, no fudging just pure geometry. Do you want to do a trade?

[@spiplayz6503]

Can i have a shout

[@DanielJosvai]

Awesome video Angus! :) I read the paper and gave it a try to model it solidworks and it was actually party easy. SW has a 'variable radius fillet' function, so I just had to make the base shape out of the for spheres, calculate the max radius and pattern the fillet to all edges. Printed a couple of them and they are mesmerizing! If you'd like to print them, you'll find the files here: drive.google.com/folderview?id=1Qy-93HJuOQZx4HiLVvJfFkszHfmj85S1

[@user-pv2ql7xk5t]

Link is not working. Can you please send the files again?

[@spiplayz6503]

I was the 7th

[@IgorEnot]

Good advertising, but you promised a video, how to make them in Fusion 360, 4 months have passed, where is it?

[@MonkeyBall2453]

"Envelope of Spheres" by which he means a radius.

[@EdgarInventor]

A big, fat, MEWAHAHAHAHAHA, of Manic enthusiasm, this time.

[@_droid]

From a mathematical standpoint it's interesting but from a practical standpoint I don't see what the big deal is. A regular old sphere is orders of magnitude better. So these don't really make any sense.

[@MakersMuse]

Can't say there's any practical purpose, it's more cool because it's possible. To me at least!

[@dinosaurus4189]

Umm, the rotary engine example was a practical application.

[@Al_Fel]

It's interesting and I enjoyed the video but surely a sphere is the ultimate solid of constant width? Is there any reason you didn't mention them?

[@looksez8621]

really starting to think you're literally trying to reinvent the wheel lol

[@robo1540]

just use spheres lmao

[@boehrb]

Too much ad. Much video selectivity in said ad.

[@22eastzenro]

Width

[@22eastzenro]

Width width width width now it knows it

[@sprocastersprocaster]

smoke dmt