The “Diagonals in SPACE” interjection might be the best highlight for this channel in a while. And I’m glad to be a part of it when it becomes a happy meme. :)
If you want Steve's subscribers, you need to fill that thing with water. You were so close! 😄 I really dig how your personality and style come through even in the bits other people help you with these days. Been a fan of yours for many years, you always bring me smiles, quite a few belly laughs and a ton of inspiration
@@robinsparrow1618 Jean-Luc Godard was a famous French filmmaker. One of the many things he was noted for was having English subtitles that were frequently different from the spoken French soundtrack of his films. These were not slight differences in the translation, they contained different storylines, conversations, and descriptions of what was happening. They were frequently written by literary authors he'd invited and they were told just to view the movie and write their own script that went along with the visual film and not to worry about what the original French film was about. He was a legendary innovator and invented the "jump cut" film transition among many other things. I didn't mean to imply this was actually stolen, this was meant as a humorous joke.
13:34 the convex hull of the 5 octahedron compound is the icosidodecahedron. I know this video is about regular dodecahedrons, but I was a little sad when you brushed it off. It’s my favorite compound, my favorite stellation, and my favorite faceting. It also looks a whole lot like my one of my favorite polyhedra, the disdyakis triacontahedron!
This was so much fun to watch and in my opinion one of Matt’s best in terms of pure enjoyment and entertainment. Matt’s enthusiasm is totally infectious and a delight to watch. The brilliant choice of music only added a new dimension (!) and I cannot praise this video enough!
Discovering the square within the dodecahedron reminds me of the end of this demonstration of the Cross Sections app: ruclips.net/video/2uHfFp1XCPc/видео.html Let me know if a tool like that could aid in visualization. You could possibly do a follow-up on the hexagon within the hexahedron.
@@needamuffin oh yes, in fact, that is also a result of same connection between the symmetry groups. (the icosahedron is duel to the dodecahedron, and three orthogonal planes have an associated cube)
Every d12 I own (which is 2, I'm not a weird dice hoarder) has the cube shape drawn on in sharpie, it's so satisfying to look at. I also like how the pieces you'd have to "cut off" to make the dodecahedron into a cube are shaped like little rooftops.
The smaller solids left behind by the shapes discussed are super satisfying in their proportions too, both the sort of flattened, obliquely truncated triangular prism you get from cutting along the square/cube and the frustrum of a pentagonal pyramid cut off by the near-equatorial pentagon...
I like several of the integrated shapes. Discovering the square within the dodecahedron reminds me of the end of this demonstration of the Cross Sections app: ruclips.net/video/2uHfFp1XCPc/видео.html
Fun fact: Both the small stellated dodecahedron and the great stellated dodecahedron can be thought of as 3D versions of a pentagram. They are both very cool shapes.
I absolutely adore the visual representation of the see through dodecahedron with the tape to show the square, pentagons etc! it's just such a satisfying visual proof of the lengths of the space diagonals
Matt, you are honestly a master educator. I'm in my thirties and failed nearly every math class I ever took (and whatever I did manager to learn, I promptly forgot when I graduated high school). Every time I watch one of your videos I learn something and I'm able to truly understand and retain concepts that boggled my mind before.
When I started learning 3D modeling and animation on the Amiga circa 1988, one of the bigger challenges I set for myself was modeling and animating regular pentagonal dodecahedron with a raised star on each face (similar to the Chrysler logo) -- thus the dodeca-deathstar was born. A couple years later, working in high end video post production, I used the mathematical precision of the amazing Ampex digital optics device with a precise pentagon matte to layer a spinning dodecahedron with different video on each face -- calculating exact angles and depth offsets with an HP-15c calculator was a wonderful challenge that grew my maths skills considerably. Sorry Matt, but the platonic dodecahedron is, and always will be, the BEST dodecahedron.
I've always loved the regular compounds and their beautiful symmetry. When I built my first raytracer and figured out how to raytrace cylinders, the compound of 5 tetrahedra (which is my favorite) was one of the first things I made a render of. The regular compounds were the first things I printed when I first got my hands on a 3D printer. Great video as always!
4:25 This diagram is the longest space diagonal, not the medium-sized one Matt is talking about in this segment. But the length (phi^2 = phi + 1) is correct for the medium-sized one!
I had to make a geometric solid out of paper as a highschool project. I chose a dodecahedron and it was pretty wild finding out that the whole net can be constructed (with straightedge and compass) using just a unit side and like 3 or 4 powers of the golden ratio. Imagine unfolding one half of the dodecahedron into a flower shape. That flower is bounded by a pentagon that's phi^2 larger than the faces.
One thing to do would be to also tape the insides, but wait, there's more... you could have taped each cube with a tape (or drew with a marker) that reacts to a different wavelength of UV. Then by switching different blacklights you could switch between the cubes instead of having them on all at the same time.
I almost audibly gasped when you taped that square on. This was a really cool way of showing everything, better even than a 3d animation or something I think.
The subtle joke for diagonals in space about 4 minutes in was really good. I imagine you were thinking, this is a bit silly, no one’s gonna even care. I care. That caught me off guard.
The first time Matt had a collab with Adam, he referred to him as "Adam Savage from Mythbusters". In return, Adam Savage referred to Matt as "Matt from Numberphile".
@@wierdalien1 Numberphile is a collection of math. Was Matt in the first video? Are they friends? (those are rhetorical) Numberphile is a channel. Matt is a guest on their channel.
That's a lovely, easy to visualize, and excellent way to explain these conceps. Absoulytely a great example of how to teach a concept really well. Good job, Matt.
Matt thanks for running the only math channel I've found that will always explain things in a way that makes sense and makes me laugh every time! I've been watching your videos for a long time and you've only gotten better with time!
The compound polyhedron made of a pair of intersecting regular tetrahedra, is aka the "stella octangula." It was a favorite of Johannes Kepler, the guy who fiddled around with the 5 Platonic solids to try to explain the relative sizes of the planetary orbits, and the guy who formulated the famous "3 Laws of Planetary Motion" that bear his name. Anyway, the 8 vertices of the stella octangula are the vertices of a cube. Which also explains the 10 regular tetrahedra in the regular dodecahedron, once you've highlighted the 5 cubes in it. Fred PS. Also interesting to note, is that the main (longest) diagonal of an n-dimensional hypercube of unit edge, is √n.
I have to be honest, I really like the stella octangula (the compound of two tetrahedra) just because it has a simplicity that a lot of the other regular compounds don't have. You can take a single glance at it and instantly know how it's constructed.
What a lovely coincidence I'm building nested platonic figures in bamboo sticks (up to 3m) with my students at the moment and analyzing this video is their homework. Thanks, Matt.
6:45 the coolest part of this was that this was wholely unsurprising thanks to your previous videos on the rhombic dodecahedron It's lovely when one maths investigation is helpful in understanding a completely unrelated one
I love the ones where you can tell how much fun he had with it, and also where the concepts don't fly too far above my head. Also I can see myself making a shitty scaled down version of this in the future.
This video made me realize why I’m not a mathematician. I can fully understand why a square being a integral part of a dodecahedron is fascinating to some people, but i literally said out loud in a room by myself “oh, I don’t like that”. I find it supremely uncomfortable.
A cube with roofs on the faces? So that the roof planes of one face continously match up with the roofplanes of the neighbour faces. Or the triangle part of one roof matches up with the trapezium part of another roof to make the pentagon without any kinks. LOVE IT!
another fun way to build a dodecahedron take a bunch of inflatable tubes (innertube , donut , torus) and lash them together i managed to build all of the solids except for the icosahedron it collapsed on itself you end up with some very large pool toys
I can solve a megaminx, so I've spent a long time looking at dodecahedra. I noticed long ago that at a certain orientation you can find a set of 6 edges that are parallel to one of the 3 axes and you can therefore make those edges all line up with a face of a circumscribed cube. It's really cool to see the numbers behind an inscribed cube. 14:00 I think I know how to create all of them. You can make the double tetrahedron with the medium space diagonal of the dodecahedron, aka the face diagonal of the cube. You might even be able to get the fifth using cube-octahadron duality. I believe this would be drawing diagonals between the edges of the dodecahedron, specifically the 6 edges mentioned in paragraph 1
One good way of investigating the relationships among the vertices, edges and faces of polyhedra is to use your favorite 3D graphics program to create a model of one, rotate it into various positions, and project the points and lines onto a plane using a parallel projection. It's easy to find perpendiculars to the faces by using the cross-product (a vector operation) of points on the edges (e.g., the vertices). The perpendiculars can then be used to orient the polyhedron appropriately. I've done some work involving polyhedra, including plans for cardboard models, which are available for free, if anyone's interested. One of my main sources of information has been the book "Mathematical Models" by A.P. Rollett and H. Martyn Cundy, which is one of my favorite books.
9:20 "The shape we were trying to made was the compound-5-intersecting tetrahedra. Here is a picture [...] and I've actually got a little print out over here" - am I the only one who was a bit sad that it wasn't a 3D print?
Love this, fantastic work! If you built this shape in a wire frame with open faces, you could use R/G/B yarn to 'trace out' all of the interior/intersecting solids and then shine contrasting RGB lights to highlight which yarns/shapes you want to stand out/disappear.
I’ve actually made an origami five intersecting tetrahedra! It took an incredible amount of time, patience, concentration, and practice with the pause button, but I did it without messing it up! I can appreciate the DIAGONALS IN SPACE a little better now.
I never really liked dodecahedrons... until now. They may not be as fun as a Truncated ditrigonary dishecatonicosachoron or as endearing as a Gyrotunnelled truncated cube, but I absolutely love how the ratios work out.
This is very similar to a personal project I wanted to tackle back in college. The years have passed and I haven’t completed it. But I was finding unique skew pair line segments within Platonic solids, to then connect their vertices to make tetrahedra. I found the Cube has 1 chiral pair of tetrahedra, and the octahedron has only one! I never made it to the Dodecahedron nor the Icosahedron… I would love if you explored this more!!
This reminds me of the 3 golden ration rectangles in the middle of a icosahedron. I'm not a mathematician so I don't have as much reference. I was teaching myself how to make stuff in CAD and looked up how to build the Polygon's needed for dice. I just remember the cube &golden ratio rectangles to make the dodecahedron and the golden ration rectangles for the icosahedron.
the autotuned "but i couldnt be bothered" cracked me up, this is why matt is the best
4:29 ϕ×ϕ this is my new favourite emoticon!
Fun fact: by definition, φxφ=Φ+1
🤯
фхф
ϕwϕ
classic cat eyes
¯\_(Φ×Φ)_/¯ - PARKER DIAGONAL IN SPACE!
The “Diagonals in SPACE” interjection might be the best highlight for this channel in a while. And I’m glad to be a part of it when it becomes a happy meme. :)
Matt still trying to make us forget about the Parker Square.
But we will never forget. :D
I was expecting a more Piiiiigs iiiiiiin Spaaaaaace vibe.
Clearly Science Asylum inspired, if you ask me. Not that I'm complaining.
The quiet echoey "space" at 3:45 killed me 😭😭😭💝💝💝
My condolences to your family.
@@Elesario than you, its so sick how you still have access to RUclips in the afterlife, didn't expect that 💝💝💝
Was about to comment this hahaha great attention to detail
I love dodecahedrons but our relationship will always be platonic
Groan... but also cute.
Perfect pun
nice
What a shame, I thought things were just golden.
That would break plato's heart, he thought the dodecahedron would always be your everything
4:42: maybe tropic would be a better word than equator, as there are two of them parallel and equidistant from the central plane.
D I A G O N A L S
I N
S P A C E
sadly youtube bitrate compression messes with my full enjoyment of D I A G O N A L S I N S P A C E
🛸👾
It is just a blatant theft from Science Asylum, but I'm not even mad. Well done by Parker-man.
@@Yezpahr nah, clearly it's blatant theft from The Muppets
I'm sure Adam Savage is a man. I'm tired of the misuse of my language by an elite few, who are trying to spread the misuse.
Great job on emulating the old educational film aesthetic for those insert animations, really sent me back...
I think a reference to Look Around You
It reminded me of the animated sequences from the classic BBC Hitchhiker's Guide to the Galaxy TV series
Excellent. I especially liked the D I A G O N A L S I N S P A C E.
If you want Steve's subscribers, you need to fill that thing with water. You were so close! 😄
I really dig how your personality and style come through even in the bits other people help you with these days. Been a fan of yours for many years, you always bring me smiles, quite a few belly laughs and a ton of inspiration
1:31 Alex, do you want to give me a hand with this?
Alex: Sure
Caption: No
made me think I was insane since I had to scroll so far to find this 😭
Shamelessly stolen from Jean-Luc Godard.
@@2ndfloorsongs who?
@@robinsparrow1618 Jean-Luc Godard was a famous French filmmaker. One of the many things he was noted for was having English subtitles that were frequently different from the spoken French soundtrack of his films. These were not slight differences in the translation, they contained different storylines, conversations, and descriptions of what was happening. They were frequently written by literary authors he'd invited and they were told just to view the movie and write their own script that went along with the visual film and not to worry about what the original French film was about.
He was a legendary innovator and invented the "jump cut" film transition among many other things.
I didn't mean to imply this was actually stolen, this was meant as a humorous joke.
@@2ndfloorsongs oh ok, this is actually really interesting and cool to know about. and it's a good joke with this context, thank you
I see that VFX department got a raise recently
Timing department getting their budgets slashed
Oh god the SFX budget went sky high for this video!
One might even say it is IN SPACE
13:34 the convex hull of the 5 octahedron compound is the icosidodecahedron. I know this video is about regular dodecahedrons, but I was a little sad when you brushed it off. It’s my favorite compound, my favorite stellation, and my favorite faceting. It also looks a whole lot like my one of my favorite polyhedra, the disdyakis triacontahedron!
The icosidodecahedron _is_ its convex hull. I don't know what Matt was talking about, maybe he meant that the convex hull is not regular.
@@galoomba5559It really sounds like he accidentally skipped a word.
7:43 It's the "Parker Fluorescent Embedded Cube", he's done it again!
I was not prepared for the joke at the end. Well done.
This was so much fun to watch and in my opinion one of Matt’s best in terms of pure enjoyment and entertainment. Matt’s enthusiasm is totally infectious and a delight to watch. The brilliant choice of music only added a new dimension (!) and I cannot praise this video enough!
agreed
Everyone taking about "diagonals in space" but 11:41 is the best voice sample for an EDM song.
And what about the "but I couldn't be bothered" from 7:47?
@@wyattstevens8574they couldn't be bothered to mention it
Hot take: _Howard Carter's entire soundtrack_ for Matt's entire channel is, like, the only _good_ EDM I've ever heard.
8:00 the rotation due to parallax and the actual rotation cancel out briefly. very cool to see
Discovering the square within the dodecahedron reminds me of the end of this demonstration of the Cross Sections app: ruclips.net/video/2uHfFp1XCPc/видео.html
Let me know if a tool like that could aid in visualization.
You could possibly do a follow-up on the hexagon within the hexahedron.
The cube dodecahedron relationship is like, my favorite thing about 3d geometry, its so beautiful
Mine is the three orthogonal golden rectangles forming the verticies of the icosahedron.
@@needamuffin oh yes, in fact, that is also a result of same connection between the symmetry groups. (the icosahedron is duel to the dodecahedron, and three orthogonal planes have an associated cube)
Every d12 I own (which is 2, I'm not a weird dice hoarder) has the cube shape drawn on in sharpie, it's so satisfying to look at.
I also like how the pieces you'd have to "cut off" to make the dodecahedron into a cube are shaped like little rooftops.
The smaller solids left behind by the shapes discussed are super satisfying in their proportions too, both the sort of flattened, obliquely truncated triangular prism you get from cutting along the square/cube and the frustrum of a pentagonal pyramid cut off by the near-equatorial pentagon...
I like several of the integrated shapes. Discovering the square within the dodecahedron reminds me of the end of this demonstration of the Cross Sections app: ruclips.net/video/2uHfFp1XCPc/видео.html
Oh, yeah! I have Steve's last video on the "watch later" list but I always forget that list.
Thanks for reminding me, Matt!
12:00 a good excuse for drawing 12 pentagrams on a dodecahedron
Matt is summoning something in the exact center of the dodecahedron so that he can trap it
Fun fact: Both the small stellated dodecahedron and the great stellated dodecahedron can be thought of as 3D versions of a pentagram. They are both very cool shapes.
All hail Satan^12.
@@Bluesine_Rwell, duh!
How else would you trap a demon in the centre?
The dodecahedron is slowly de-throning the icosahedron from being my favorite platonic solid, thanks to crazy fun stuff like this.
I absolutely adore the visual representation of the see through dodecahedron with the tape to show the square, pentagons etc! it's just such a satisfying visual proof of the lengths of the space diagonals
I couldn't be bothered marking the insides translates to "I gave it a go". Totally a parker cube.
Matt, you are honestly a master educator. I'm in my thirties and failed nearly every math class I ever took
(and whatever I did manager to learn, I promptly forgot when I graduated high school). Every time I watch one of your videos I learn something and I'm able to truly understand and retain concepts that boggled my mind before.
When I started learning 3D modeling and animation on the Amiga circa 1988, one of the bigger challenges I set for myself was modeling and animating regular pentagonal dodecahedron with a raised star on each face (similar to the Chrysler logo) -- thus the dodeca-deathstar was born. A couple years later, working in high end video post production, I used the mathematical precision of the amazing Ampex digital optics device with a precise pentagon matte to layer a spinning dodecahedron with different video on each face -- calculating exact angles and depth offsets with an HP-15c calculator was a wonderful challenge that grew my maths skills considerably. Sorry Matt, but the platonic dodecahedron is, and always will be, the BEST dodecahedron.
I've always loved the regular compounds and their beautiful symmetry. When I built my first raytracer and figured out how to raytrace cylinders, the compound of 5 tetrahedra (which is my favorite) was one of the first things I made a render of. The regular compounds were the first things I printed when I first got my hands on a 3D printer. Great video as always!
Are you THE Matt Parker from the Parker Square? What an honor!
4:25 This diagram is the longest space diagonal, not the medium-sized one Matt is talking about in this segment. But the length (phi^2 = phi + 1) is correct for the medium-sized one!
Thanks, I paused and looked for this comment.
phi^2 = phi + 1
Golden ratio quadratic equation.
Ben: Hey Matt! I've made a spinning dodecahedron in Geogebra!
Matt (after this video): I don't need you anymore! I can make my own spinning polyhedra!
the editing on this is impeccable
I had to make a geometric solid out of paper as a highschool project. I chose a dodecahedron and it was pretty wild finding out that the whole net can be constructed (with straightedge and compass) using just a unit side and like 3 or 4 powers of the golden ratio. Imagine unfolding one half of the dodecahedron into a flower shape. That flower is bounded by a pentagon that's phi^2 larger than the faces.
One thing to do would be to also tape the insides, but wait, there's more...
you could have taped each cube with a tape (or drew with a marker) that reacts to a different wavelength of UV. Then by switching different blacklights you could switch between the cubes instead of having them on all at the same time.
Are we sure there is such a product?
8:32 it tickles me no end to learn that Matt is a Look Around You fan
There is something SO satisfying about those taped models. Thank you.
your videos are capable of pulling one out of depression and make them fall deeper in love with mathematics. Thanks a lot for your work, sir.
Legend says that he still says "Diagonals in Space"
I almost audibly gasped when you taped that square on. This was a really cool way of showing everything, better even than a 3d animation or something I think.
Once again, you're knocking it out of the Parker with these videos!
"Lots of ridiculous maths things" .... is possibly the best description of this channel I have heard ....
8:24 matt's mental maths is on point
7:40 this is next level editing XD
3:30 I immediately know where this video is going and I love it!
The subtle joke for diagonals in space about 4 minutes in was really good. I imagine you were thinking, this is a bit silly, no one’s gonna even care. I care. That caught me off guard.
You should be honest - "You might know me from Numberphile video with the Parker Square"
The first time Matt had a collab with Adam, he referred to him as "Adam Savage from Mythbusters". In return, Adam Savage referred to Matt as "Matt from Numberphile".
Adam was with mythbusters. Matt isn't with numberphile...
@CBWP I mean he is, he has been doing videos since the start
@@wierdalien1 Numberphile is a collection of math. Was Matt in the first video? Are they friends? (those are rhetorical) Numberphile is a channel. Matt is a guest on their channel.
@@CBWP yes and yes and yes.
That's a lovely, easy to visualize, and excellent way to explain these conceps. Absoulytely a great example of how to teach a concept really well. Good job, Matt.
I aspire to enjoy my work as much as Matt
Matt thanks for running the only math channel I've found that will always explain things in a way that makes sense and makes me laugh every time! I've been watching your videos for a long time and you've only gotten better with time!
Turning obscure math into real world objects, keep up the good work Matt!
I love the over-the-top editing style.
Just goes to show how you can't please everyone. I hate it.
The compound polyhedron made of a pair of intersecting regular tetrahedra, is aka the "stella octangula."
It was a favorite of Johannes Kepler, the guy who fiddled around with the 5 Platonic solids to try to explain the relative sizes of the planetary orbits, and the guy who formulated the famous "3 Laws of Planetary Motion" that bear his name.
Anyway, the 8 vertices of the stella octangula are the vertices of a cube.
Which also explains the 10 regular tetrahedra in the regular dodecahedron, once you've highlighted the 5 cubes in it.
Fred
PS. Also interesting to note, is that the main (longest) diagonal of an n-dimensional hypercube of unit edge, is √n.
I always was a fan of the Icosahedron, but this video made me appreciate the Dodecahedron.
I have to be honest, I really like the stella octangula (the compound of two tetrahedra) just because it has a simplicity that a lot of the other regular compounds don't have. You can take a single glance at it and instantly know how it's constructed.
What a lovely coincidence I'm building nested platonic figures in bamboo sticks (up to 3m) with my students at the moment and analyzing this video is their homework. Thanks, Matt.
6:45 the coolest part of this was that this was wholely unsurprising thanks to your previous videos on the rhombic dodecahedron
It's lovely when one maths investigation is helpful in understanding a completely unrelated one
I love your visualization, it makes the whole thing insanely well understandable for me
I love the ones where you can tell how much fun he had with it, and also where the concepts don't fly too far above my head. Also I can see myself making a shitty scaled down version of this in the future.
Good ol' small stellated dodecahedron and the great stellated dodecahedron
Loved the book! I love how you were able to invent *time traveling* with trig! Mark my words, This is going to be the best-selling book in history!
This video made me realize why I’m not a mathematician. I can fully understand why a square being a integral part of a dodecahedron is fascinating to some people, but i literally said out loud in a room by myself “oh, I don’t like that”. I find it supremely uncomfortable.
A cube with roofs on the faces? So that the roof planes of one face continously match up with the roofplanes of the neighbour faces. Or the triangle part of one roof matches up with the trapezium part of another roof to make the pentagon without any kinks. LOVE IT!
The editing is genius
This is one of my favorite Stand-Up-Maths video!!!!!
It hits better when you can visualize it in real life. Thanks Matt
A masterpiece of maths and editing
Thanks, Matt. Thatt.
Rollie Williams would be proud of the video's style I reckon
“Seemed clever at the start, I regretted it immediately”… that can basically be the theme of my life 😂
This was such a good visual demonstration!
another fun way to build a dodecahedron
take a bunch of inflatable tubes (innertube , donut , torus)
and lash them together
i managed to build all of the solids
except for the icosahedron
it collapsed on itself
you end up with some very large pool toys
Imma need that track. 🎶"I couldnt be bothered."🎶
i will never look at a megaminx the same way after this
Correction: graphic at 4:22 is longest diagonal = φ √3.
replying to boost the correction
This is one of the most awesome things I've seen. So much better than CGI
Did not disappoint with the Steve Mould banter.
Novice sorcerer: Pentagram on the floor, demon flies away.
Experienced Warlock: PENTAGRAM DODECAHEDRON!
great vid, and looking forward to your book and, as a UK resident, can't wait for the 6th day of 20th month to get it
man my workbook is getting full thank you for that note
I can solve a megaminx, so I've spent a long time looking at dodecahedra. I noticed long ago that at a certain orientation you can find a set of 6 edges that are parallel to one of the 3 axes and you can therefore make those edges all line up with a face of a circumscribed cube. It's really cool to see the numbers behind an inscribed cube.
14:00 I think I know how to create all of them. You can make the double tetrahedron with the medium space diagonal of the dodecahedron, aka the face diagonal of the cube. You might even be able to get the fifth using cube-octahadron duality. I believe this would be drawing diagonals between the edges of the dodecahedron, specifically the 6 edges mentioned in paragraph 1
One good way of investigating the relationships among the vertices, edges and faces of polyhedra is to use your favorite 3D graphics program to create a model of one, rotate it into various positions, and project the points and lines onto a plane using a parallel projection. It's easy to find perpendiculars to the faces by using the cross-product (a vector operation) of points on the edges (e.g., the vertices). The perpendiculars can then be used to orient the polyhedron appropriately.
I've done some work involving polyhedra, including plans for cardboard models, which are available for free, if anyone's interested. One of my main sources of information has been the book "Mathematical Models" by A.P. Rollett and H. Martyn Cundy, which is one of my favorite books.
Maybe it's because spring is coming, but I've suddenly begun noticing how adorable Matt Parker is. What a math hunk!
Easily the best polyhedral based mini-rave I’ve had all week!
The compound of 5 octahecdrons absolutely does have a convex hull. It's convex hull is the icosidodecahedron, an archimedean solid.
9:20 "The shape we were trying to made was the compound-5-intersecting tetrahedra. Here is a picture [...] and I've actually got a little print out over here" - am I the only one who was a bit sad that it wasn't a 3D print?
Love this, fantastic work! If you built this shape in a wire frame with open faces, you could use R/G/B yarn to 'trace out' all of the interior/intersecting solids and then shine contrasting RGB lights to highlight which yarns/shapes you want to stand out/disappear.
There are, in fact, more than 5 regular polyhedra! jan Misali has a great video on this, titled "There are 48 regular polyhedra" if I recall correctly
the editing is amazing!!!
I’ve actually made an origami five intersecting tetrahedra! It took an incredible amount of time, patience, concentration, and practice with the pause button, but I did it without messing it up!
I can appreciate the DIAGONALS IN SPACE a little better now.
It is a very beautiful shape, I'm not sure whether I like the visualization of the single nested cube or the 5 cubes making pentagram faces more.
I never really liked dodecahedrons... until now. They may not be as fun as a Truncated ditrigonary dishecatonicosachoron or as endearing as a Gyrotunnelled truncated cube, but I absolutely love how the ratios work out.
This was mind blowing, definitely one of my favorite Matt videos. Almost cool enough to make me unsubscribe from Steve Mould.
This is very similar to a personal project I wanted to tackle back in college. The years have passed and I haven’t completed it. But I was finding unique skew pair line segments within Platonic solids, to then connect their vertices to make tetrahedra. I found the Cube has 1 chiral pair of tetrahedra, and the octahedron has only one! I never made it to the Dodecahedron nor the Icosahedron… I would love if you explored this more!!
Adding new shapes to the friends list!
We want a t shirt of this with text "Diagonals IN SPACE"
Matches his Rubik's dodecahedron in the background. Neat.
Brilliant example of fairly simple geometry being done really, really beautifully, love the UV :)
This reminds me of the 3 golden ration rectangles in the middle of a icosahedron. I'm not a mathematician so I don't have as much reference. I was teaching myself how to make stuff in CAD and looked up how to build the Polygon's needed for dice. I just remember the cube &golden ratio rectangles to make the dodecahedron and the golden ration rectangles for the icosahedron.
I like that he took the time to build a Dodecahedron instead of just showing us a 3D model :D