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!
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!
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!
If your goal were smoothness (which it might not be), there are improvements over this one. You can get G2 smoothness across the edges on top of perfect tetrahedral symmetry. Though perhaps, in terms of style, the sharp edges of this version actually make for something prettier overall?
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.
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!
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.
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: th-cam.com/video/hYeVAmyu7Ow/w-d-xo.html 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.
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
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.
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.
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.
@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.
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
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?
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.
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
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.
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.
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
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?
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
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?
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.
This dude will freak when he finds out about spheres!
No
No to what part?
I’m confused.
@@tarrute freak out
woosh?
If this is the ultimate solid of constant width, where would you place the sphere?
Thanks. I decided to check the comments 'cause that was EXACTLY what was in my mind XD
Sphere would be trivial solid of constant width..
If this is the ultimate, the sphere is clearly the first one.
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.
In the future, you may want to refrain from asking most internet comment sections as to where you should put a spherical object
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!
Thanos: forget everything in perfect Balance,
a Solid of Constant width, is the new thing now .
perfect constant width as all things should be
Have you tried Googling the word Thanos and clicking on the glove?
licensetodrive ye I ha
That intro with the unique rolling objects would have Tim from Grand Illusions saying, "uh, what fun!".
Yah
drinking game - take a shot everytime he says "constant width"
You got me obsessed with solids of constant widths a few years ago. Ever since then, I can't get over with them!
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!
I need some dice based on these shapes.
*and some say he is still rolling to this day*
It would only work if it had a weight in a cavity shaped like the dual of the shape
Thanks I’m staying awake all night now. damn you (not really)
This man made me fall in love with these crazy shapes
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!
That is oddly satisfying :O
Wow, and the project rolls off again😀👍
Thanks for sharing this👍😀
If your goal were smoothness (which it might not be), there are improvements over this one. You can get G2 smoothness across the edges on top of perfect tetrahedral symmetry.
Though perhaps, in terms of style, the sharp edges of this version actually make for something prettier overall?
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.
could your replace your tires with them ?
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!
yiou would bavebyahey
Wow, this was an interesting video. Thanks.
Really cool Angus! Thanks.
Great video Angus, looking forward to more on this enthralling subject and what you do with it.
Oh my, they are gorgeous, such beautiful symmetry and absolutely amazing. Thanks for the video.
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.
I think I need to make a d4 of constant width.
You would need a pretty tough surface to roll these bad boys! Would work pretty good though.
@@MakersMuse yeah I like to use leather lined trays or dice towers for this.
How about a unique surface that allows a standard D6 to roll like a sphere.
@@amoose136 tricky, but maybe doable. In 2d its no problem. But how would you read your dice ^^
It would be an unfair die though
That's so awesome that they contacted you !
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: th-cam.com/video/hYeVAmyu7Ow/w-d-xo.html
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.
Beautiful video. Thanks
Now i wanna see other solids of constant width based off of the other platonic solids
Thank you for making me get a 3D printer, it was worth it!
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
Here's one that's already finished. www.kickstarter.com/projects/ghrostyschuff/roloids-solids-of-constant-width/updates
*Watch this on x2 its better!*
I love your background music, it reminds me of the early work by Rameses B-
Absolutely amazing. If you can perfect the printable stl, it will be worth buying.
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.
Angus it's a 50 pence piece not Cent
The 50 Cent piece is just a round gold coin
Just backed the Kickstarter for a steel one : $28 plus $5 shipping
Total sucker compliant mechanisms and cool shapes.
Thumbnail: "perfection at last"
Me: ohhh so that's what the gamesphere 2 will look like.
Maybe easier to define in OpenSCAD?
I would like to take a swing at that.
Was going to give it a crack, but a quick google saved me the time: ceptimus.co.uk/?p=345
Couldn't resist: www.thingiverse.com/thing:3620748 - combines the fairly efficient code of ceptimus with the symmetry of xtalgrafix
@@TroyMackay I think you might have too much symmetry. According to that reference "Note that only three of the edges are rounded"
@@bobmvideos In the original ceptimus code, yes. Not in the xtalgrafix maths I implemented on top.
The 'un-ball' bearing
Fun party game: take a shot everytime he says solid(s) of constant width
Could you do the sphere sweep to any platonic solid for the same effect?
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.
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.
Beautiful!
@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.
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
Wow downright spiritual
Very interesting stuff, mate, thanks for sharing !
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?
A sphere is a particular case of a solid of constant width, that also has constant radius.
Use these as bearings!
Ultimate sexiness like Angus
I did a drinking game on every "solid of constant width" and can't feel my legs anymore now
I wonder how these would work as a 4 sided die
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.
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
Your interest is kind of interesting
Final video about solids of constant width... to be continued.
Is this not a Meissner Tetrahedron? Are all 6 edges of the Reuleaux Tetrahedron modified here?
Does it required support material to print?
A solid of constant width, not to be confused with the solid of constant girth. Also known as Big Chungus
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.
Ok. I want one it those.
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...
I wrote an openscad script to show this construction a while back www.thingiverse.com/thing:2323357
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.
I love your passion. I can only strive to make similar good content. However I am more a DIY channel
Hi, would you be able to do a review of the CoLiDo DIY 3D printer?
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
I'm wondering if you could do a 3D scan of those and then print them out.
Oh, it's a spheramid (and definitely not a shining trapezohedron)!
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?
I want a meissner tetrahedron... can't find any
I feel you. I often feel like a strange geometric object. 🤣
Dorito Jesus
How about a solid of constantly variable width.
Wait, a reuleaux tetrahedron is not a solid of constant width‽ why?
Wikipedia has the answer I believe. I didn't check the proof yet so can't explain it to you myself.
This was a tasty video! What would be a better way to say that?❤
I need help.
I am looking for s good 3D printing Surface with the size of 310mmx310mm-330mm330mm
Mmmm rotary engine!
Can you make an antweight combat robot please.
constant THICC !!!!
Think twice before you back this on kickstarter and do some homework.
can we get angus 2 half a million?
But a riuleaux triangle is a three dimensional example of an object of constant width..
1:00 kinda also looks like an israeli 5₪(shekel) coin
please PLEASE build a 3d printed wankel rotary engine that would be so cool🤤
Backed :)
that's to much super girl for me lol. nice vid
What is this witchcraft?
It's not a ball how does it work?
Good advertising, but you promised a video, how to make them in Fusion 360, 4 months have passed, where is it?
Yay
A big, fat, MEWAHAHAHAHAHA, of Manic enthusiasm, this time.
Hi bro
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
Link is not working. Can you please send the files again?
Can i have a shout
just use spheres lmao
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?
Too much ad. Much video selectivity in said ad.
really starting to think you're literally trying to reinvent the wheel lol
I was the 7th
Width
Width width width width now it knows it
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.
Can't say there's any practical purpose, it's more cool because it's possible. To me at least!
Umm, the rotary engine example was a practical application.
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?
"Envelope of Spheres" by which he means a radius.
smoke dmt