What Links Dice and Tesseracts? | Machining the Platonic Solids

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In this video, we machine the 3D platonic solids and explore these polyhedrons in higher dimensions. Hazel talks through the history of these fascinating shapes and reveals interesting facts along the way.
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Attributions:
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4D model animations: robertlovespi.net/ and en.wikipedia.org/wiki/User:Ja...
3D-printed models: www.thingiverse.com/thing:84389, grabcad.com/library/120-cell-1, www.thingiverse.com/thing:185...
Kepler Platonic Solids Image: commons.wikimedia.org/wiki/Fi...
Dymaxion map: en.wikipedia.org/wiki/File:Dy...
Mercator map: en.m.wikipedia.org/wiki/File:...
Folding nets: es.wikipedia.org/wiki/Usuario...
Toluca Meteorite: commons.wikimedia.org/wiki/Fi...
Dodecahedron universe paper: www.researchgate.net/publicat...

[@ENDESGA]

as a platonic solid myself, I approve of this video

[@abov2983]

TYPICAL

[@pizzapig97]

I love the change of narration. It is such a sweet addition, I feel so soothed by her voice. Wonderful work.

[@NoelBarlau]

Now that took some planning and execution for the manual machining. Well done to Alistair. And even if nobody else appreciates it, I noticed the hand-scraped mill table. Those machines have seen some loving and detailed restoration.

[@ManSkirtBrew]

Thumbs up for hexagons are bestagons reference!

[@douglasharley2440]

clearly, hazel is as good at math as alistair is at machining! *respect*

[@TalRohan]

having made a tetrahedron in wood by hand many years ago I can definitely appreciate just how difficult they are to construct..I can't imagine doing the others by hand . Fascinating and weird stuff Thankyou for sharing

[@robertogrady1321]

Thanks for the video. I'm afraid the explanation went straight over my head but I understood all of the machining.

[@FredStam]

what an interesting video, fine craftmanship

[@johngentzel115]

Greetings, I came over from Tested where Adam Savage gave you some huge props. Looking forward to going thru your prior videos.

[@chronovaengineering]

Thank you for having a look at our channel. We hope you enjoy the content!

[@aarocka11]

My favorite Platonic solid is a Utah Teapot

[@leftaroundabout]

Nah, the Utah Teapot is too difficult to machine. I prefer Russel's Teapot, I can easily make that on a lathe. What, you don't think I can? You'd better prove it!

[@aarocka11]

@@leftaroundabout who teapots the teapot?

[@goten2831]

amazing channel

[@needamuffin]

My favorite fact about the icosahedron is that you can construct it using three orthogonal golden rectangles. The verticies of the rectangles are the verticies of the icosahedron.

[@jimsvideos7201]

Great fun, and my regards to the narrator for her charming contribution.

[@smizmar8]

Excellent hexagon reference! They really are the ....

[@donaldasayers]

The rhombic dodecahedron is a doddle to machine, it can be milled directly out of hex stock.

[@theenchiladakid1866]

I didn't understand any of that but i enjoyed hearing it

[@DanielMoraPhoto]

Angry Kepler and Pythagoras noises intensify!

[@kimmy_future4265]

Ok, what a weird coincidence. I just saw a post about the roman dodecahedrons less than an hour ago with the knitting explanation and now it came up again. It must be a sign lol. Of what though, i have no idea haha.

[@phoenixrahillconghaile7320]

Wondering how the 3d model for the 120 cell was made? Is it generated mathematically?

[@madcapmagician6018]

you guys just made a complete set of D&D dice =P lol

[@noanyobiseniss7462]

I'm unable to imagine the 4th dimension unless it is being considered as time and doubt anyone else that is locked within 3d space can either.

[@mediocrefunkybeat]

Unless you're Andrew Wiles...

[@noanyobiseniss7462]

@@mediocrefunkybeat I bet if you ask him whether he can he will state that he cannot.

[@gaveintothedarkness]

How about the 5th dimension?

[@noanyobiseniss7462]

@@gaveintothedarkness I did read hyperspace in the 90's and did a paper on it and while I can see(sense) waves I cannot fathom shapes.

[@gaveintothedarkness]

@@noanyobiseniss7462 Actually....I was making a joke. There is a band called 5th dimension and they sing the song "age of aquarius" :P

[@user-yx6iv8sq9t]

are they for sale?

[@JSAnstock]

I think it's pretty obvious that the Roman dodecahedrons were early incursions into table top rpg's. After all, didn't Julius Caesar say "Alea iacta est" 😉

[@john1182]

im here from Adam Savage, im glad i was sent across

[@RichardBronosky]

What was the source of the narration?

[@NonEuclideanTacoCannon]

I've seen the animated representations of a tesseract before, and I'm honestly not sure what I'm looking at, what it is representational of. Like, is the suggestion that if such a thing actually physically existed, it would always appear in motion like that to 3-dimensional observers? A regular cube already exists in 4 dimensions, and it isn't a writhing, headache-inducing eldritch abomination to look at. Really wish I could have afforded college.

[@leftaroundabout]

It wouldn't necessarily appear to be in motion. The easiest way to imagine a tesseract in the 3+1 dimensional space we live in is a cube that appears out of nothing at some point in time and again vanishes into nothing some time later. In that case, at each instant you have a 3-dimensional slice through the 4-dimensional tesseract, and all these slices happen to look the same (in the same way you can slice a cube into a bunch of equal square sheets). However, that means you're missing the actual interesting features of the tesseract. To understand those moving animations, consider that you're slicing a cube diagonally and stamping the cut-section onto 2-dimensional paper. The imprint will in general be an irregular hexagon. Then imagine you're doing this over and over again (slicing lots of cubes in succession), but each time you're cutting in a slightly different direction. The result of this is an animated 2D shape. Now apply the same concept to the 4-dimensional tesseract: you're slicing it diagonally, every time getting a different 3-dimensional object. Those are the objects these animation are showing.

[@NonEuclideanTacoCannon]

@@leftaroundabout Ah, I see

[@BenB21361]

13:10 "it's impossible to fold a net of hexagons into a regular 3d shape" The muoctahedron does have hexagonal faces, and I mean technically depending on what you call a hexagon some regular petrial polyhedra and the blended hexagonal tiling have hexagonal "faces". As well as some Grunbaum dress polyhedra. As for folding these from a net of hexagons, well...

[@billdoodson4232]

"Muoctahedron"! Well that led me down a rabbit hole. Wikipedia comes up with "Regular skew apeirohedron". Dear god what's regular about that? I'm sticking to 2D geometery with the odd excursion into 3D. The narration was wonderful, that lass should be on the tellybox.

[@BenB21361]

@@billdoodson4232 If you're interested in these things you might enjoy jan misali's video on regular polyhedra. I find it very amusing and interesting

[@adrianwilliams763]

Enjoyed watching the machining. Totally baffled by the narrative. Sorry Hazel, no disrespect.

[@oppsicle]

Where is old bro????

[@oppsicle]

His voice is just so soothing!!!!!

[@ernie5229]

The narrator sounds like that math girl. Is it?

[@heitorgoku]

First

[@mxecho]

noice

[@guitarchitectural]

No one cares.

[@jimburnsjr.]

please do not do instructional videos of lathe work... with jewelry on..

[@Andrew_Fernie]

it's a 6 dimensional ring which won't interact with the 3d chuck

[@Dan-oo1rj]

I'm sorry, but I prefer the previous narrator. He seemed to understand what he was saying. In addition, he didn't read so fast that he only spit out the letters and words as quickly as possible, he just gave time to enjoy the image and contemplate the description :)

[@Aesop059]

Agreed.

[@JMFuller227]

Couldn’t disagree more. What makes you think this narrator does not know what they are talking about? They were simply transparent about who was doing the machining operations.

[@guitarchitectural]

Tell me you're a misogynist without telling me you're a misogynist

[@FlakeSE]

The other “narrator” would have read the exact same script. I think the delivery was clear and properly paced for the length of the video, perhaps the script was a tad long for the video in the first place.

[@DaleDix]

​@guitarchitectural very overused and misused word.

[@craigmahan5185]

Here you go my brother! And she sounds cute!! @sevenspaulding123