The Bilinski dodecahedron, rhombic icosahedron, rhombic triacontahedron, and rhombohedron are the four unit shapes in a quasicrystal. All the faces are golden rhombi, and it has 5-fold icosahedral symmetry. Subscribed.
No, like, I want a platinum sugar packet kept in a glass container in a climate controlled vault with a code split between 3 people who live in separate countries.
One thing to mention is that if you continue the process of "removing a belt of rhombuses" with the Bilinski dodecahedron, you can actually create a rhombic hexahedron (looking like a partially squashed cube). There are actually an infinite number of possible rhombic hexahedrons (where the diagonals have a ratio between 1:1 [cube] and 1:√3 [basically a degenerate hexagon]), but the golden rhombic hexahedron is unique in that it is the only rhombic hexahedron that can "add" a belt of identical rhombi to create a rhombic dodecahedron.
Thanks Matt. I have used geometry in my craft works for quite some time, including the rhombic model. Just realised there was a big story behind it. Quite interesting indeed.
5:37 "There's the guy who stole our stuff!" Also, Croatia! I live right next to it (Slovenia)! It's probably been years since I last came across a serious mention of one or the other on the Internet. And, even now, it's not *my* country. It's just really close. What a Parker Square moment.
They say that mathematicians are people who turn coffee into theorems. Now we learn they may also turn instant coffee (and sugar and brochures) into geometric shapes ...
The main thing I learned from this video is that Mat Parker should not be left alone in a hotel room for to long without adult supervision, he'll go mad with boredom and start making strange shapes and rambles on and on on the balcony. Interesting video though.
As you can no doubt deduce from what you know about the Rhombic Icosahedron, the shape made by two opposite edges and an imaginary pair of parallel lines through the Icosahedron connecting the two opposite edges is a golden rectangle. I love polyhedrons and phi, and I literally cheered out loud when you declared that the Bilinski Rhombic Dodecahedron was made up of Golden Rhombi. I love this stuff.
My countryman and a college mathematician mr. Bilinski, although I must admit I have never heard of him. Fascinating stuff, Matt. This reminds me how I once discussed one-point compactification with a matematician during a garden party and BBQ. All we neded was a ball or an orange to point at it. :-) -- -- -- -- Keep up the good work and come again soon. Greetings from Croatia.
I love the part when the person walks onto their balcony, looks over at Matt talking about rhombic dodecahedrons to a camera, and then immediately turns around and goes back inside.
That made me so happy to see the golden ratio turn up. That's actually what I thought you were going to say about the ratio of the diagonals of the first rhombus.
omgg mat im your huge fan from croatia, cant believe you were in croatiaa, hope you had an awesome time. Judging by the hotel, you were in Dubrovnik, im from Zadar its a little farther up. Oh and btw i love physics too, i was actually 4th on the states (like the whole croatia) physics competition. love your videos byee
@standupmaths -I've been a numberphile viewer for years and have always loved your videos. Loved this one as well and keep it up; I'll keep watching. Your charismatic spin on mathematics keeps me curious (in general) and engaged in my personal betterment.
Once again, I learned something about Math!!?? Matt you are amazing. I have no idea how to use this information, but I find it fascinating, and feel smarter for the experience. Thank you
oh..em...gee... the point where you started using excel to divide the packet just cracked me up, this was a hillarious piece of umprvised geometry, very impressed
lol, here I was googling a good visualization of the Bilinski dodecahedron while thinking about how Matt would hate it for the golden ratio, and then a video by him is the first good visualization I find. I really should just subscribe to this channel already.
Timothy Warner Yes I know. But "showed up out of nowhere" is still inaccurate because he was using the golden ratio earlier. And since the lengths of the diagonals are intrinsically related to the lengths of the sides, there's even less of a reason to be surprised.
The reason to be surprised is that not every rhombus will be able to form a dodecahedron (in fact very few) and yet one of the rhombus'; that works happens to be in the golden ratio.
I enjoyed the way your neighbour popped her head out just after the 5 minute mark, and promptly went away again...and who can blame her. Also, I hope you sent this video to the Hotel - I'm sure they'd enjoy this.
Did she lock you in? You do realize that Kings Landing is on the other side of that hill? If you need more maths to do in Dubrovnik, might I recommend you solve for Pi while you dine at Lady Pi Pi. Show her a nice time since you ruined her chances at ordering in.
I am sitting here with a bag of Munchies, eating them in consistent harmony with the video. Every time Matt's voice lowers I eat one and will almost certainly be ill.
Why is it that when you add a belt to a rhombic icosahedron you don't add 8 faces to get a rhombic octaicosahedron? Why do you need to add a 10 to get the next polyhedra in the series? Is there a larger polyhedra beyond the rhombic triacontahedron? How many faces are needed to be added to construct that one? Is there a relevant sequence in OEIS describing these relationships?
found the hotel is in Dubrobnik, wonderful city i will hopefully go there next summer again. Also that "hat" looks like something Kryten could wear quite comfortably :D
BaconKwagga im not talking about the hotel staff or such. I got family there and ive lived there for a while and the people are trully nice and honest. Especially in the smaller fishing villages with small communities they really know how to enjoy life
Very cool! There is a great set of geometry blocks called 'Rhombo', created by Michael Longuet-Higgins (co-discoverer of some of the uniform polyhedra), the Bilinski dodec arises pretty naturally out of them, especially when you are trying to construct a triacontahedron.
-How was the conference honey? -It was pretty good, but it was a bit too long and I'm starving, where's the room service menu? -Yeah well, about that...Happy Rhombic Dodecahedro day! -You got bored didn't you? -Yeah...
This is so beautiful! :'D I see confusion when we talk about "rhombic dodecahedra" now... Perhaps we should rename the standard Rhombic Dodecahedron to something catchy & unique! From rho[mbus] + doz[en], I suggest calling it a Rhodoz!
Matt mentioned only four of the platonic solids having corresponding rhombic dodecahedra (in pairs of a solid and its dual). What about the tetrahedron? Well that is its own dual, so the resulting rhombi have both diagonals the same, and there are 6 edges on the tetrahedron giving 6 rhombuses, so the consequent rhombic hexahedron is just a cube!
His name was Stanko Bilinski and he was from Nasice, wich is in Slavonia. I am going to school in that city and every year we have a Stanko's geometry school.
Either "Oh, someone's making a video, let's just quietly step out of the shot" or "There's a madman talking to a strange shape, let's just back away slowly..."
You showed (among other things) rhombic dodecahedra with rhombus ratios (ratios of the two diagonals) of sqrt(2) and phi (golden ratio). Could there be other rhombic dodecahedra with other ratios that we just haven't found yet?
I really enjoyed this video as I occasionally make polyhedra myself. However you definitely get the award for geek of the year. :-) In a beautiful part of the world and you spend the whole day cooped up in your hotel room with paper and scissors. You're in a long tradition of mathematicians ignoring their environment - in some cases like Archimedes even ignoring raging battles around them. Kudos.
I find the lack of footage showing the return of the scissors and tape disturbing.
Great video!
+MadManoloz It's coming.
Still waiting
@@justitroyal7032 on the 2nd channel ;)
thief!
Who needs sleep when you can learn about Croatian Rhombic Dodecahedrons?
yeah that's where I am too
Dodecahedra :)
Obscure Croatian variants of interesting shapes > sleep
Dodecahedrii
ikr? 3am watching Matt doing his things.
5:38 you have a fan of rhombic dodecahedrons in the background there.
I can just imagine someone else in the hotel hearing you yell "CURSE YOU GOLDEN RATIO" and just being completely confused
And then looking up and seeing Matt after almost winning a game of Candy Crush and yelling out "CURSE YOU PARKER SQUARE" :P
So building almost platonic shapes counts as a Parker Solid?
a 3d version of a parker square?
That was a real Parker square of a comment, mate.
That would be a parker cube, which we should figure out what would be.
+Abdul Muhaimin a Parker cube?
+Peter LeRoy “Apl 527097” Barnes A cube with five faces
Answering the age old question of "What does a mathematician do on holiday?"
Matt Parker: Nutcase or Genius? This video is evidence for both
It's just a fine line between the two...
neither
Wouldnt say neither but hes definately smart.
+Ukid111 that didnt make sense
...but did you return the scissors and tape? :D Also, was there any tape left?
That's what I want to know
Asking the important questions!
Matt...the scissors thief? I hope not!
he certainly didn't return a lot of tape....
Another important question: did the flowers of the hotel's garden survive?
The Bilinski dodecahedron, rhombic icosahedron, rhombic triacontahedron, and rhombohedron are the four unit shapes in a quasicrystal. All the faces are golden rhombi, and it has 5-fold icosahedral symmetry. Subscribed.
Can we standardize the sugar packet as a unit of measurement? It really is the perfect size, and everyone knows how big they are.
It's called the inch :) :P
No, like, I want a platinum sugar packet kept in a glass container in a climate controlled vault with a code split between 3 people who live in separate countries.
you could start a kickstarter for that
That guy at 5:40 though :D
PS im super surprised that im so early that on my screen, there is only one comment (Aaron Howell)
I hope you mean the guy in the far back and not the lady closer to the foreground.
I hope you left those in your room and confused the hell out of the staff there
And skip out on really cool souvenirs? You don't know how to live.
Lols > souvenirs
I would have given it to the nice lady who lended the cisors and tape.
One thing to mention is that if you continue the process of "removing a belt of rhombuses" with the Bilinski dodecahedron, you can actually create a rhombic hexahedron (looking like a partially squashed cube).
There are actually an infinite number of possible rhombic hexahedrons (where the diagonals have a ratio between 1:1 [cube] and 1:√3 [basically a degenerate hexagon]), but the golden rhombic hexahedron is unique in that it is the only rhombic hexahedron that can "add" a belt of identical rhombi to create a rhombic dodecahedron.
Once again, you never disappoint me with another upload. Funny humor, great explanations and a well crafted video. Glad I subscribed!
+Kacper Bazan I'm glad you subscribed as well!
Thanks Matt. I have used geometry in my craft works for quite some time, including the rhombic model. Just realised there was a big story behind it. Quite interesting indeed.
+EzyCraft Glad you enjoyed it! I'd love to see more rhombic dodecahedron art.
Magazines, Sugar Packets, and Excel... you should totally bill yourself as the "MacGyver of Maths"
"MathGyver"
MattGyver!
Shadow81989 MatthGyver
+
This is just ridiculously silly. I love it.
Matt Parker - milking maths out if everything (including, but not limited to, sugar and roomservice menus)
Oh, and root 2 is a vastly superior ratio xP
+PassionPopsicle go A4
AX where X>=0 really, that's kind of the point
But not milk, funnily enough.
+IamGrimalkin Yet. Not milk... yet.
the guy at 5:38 is like "What is this guy doing?"
That guy has a skirt and boobs
+Lock Ray best fucking response ever! 😂
Girls can be guys too!
Couldn't see that it's a lady at first. Went back and saw it. Couldn't stop laughing :)
Wow! I thought it was a guy, too. I think maybe it's a hotel employee, looking for the scissors and tape.
5:37 "There's the guy who stole our stuff!"
Also, Croatia! I live right next to it (Slovenia)! It's probably been years since I last came across a serious mention of one or the other on the Internet. And, even now, it's not *my* country. It's just really close. What a Parker Square moment.
I hope you showed your work to the hotel lady when you were finished.
When he returned the scissors and what's left of the tape :P
UnqualifiedAdvice
Exactly!
They say that mathematicians are people who turn coffee into theorems. Now we learn they may also turn instant coffee (and sugar and brochures) into geometric shapes ...
The main thing I learned from this video is that Mat Parker should not be left alone in a hotel room for to long without adult supervision, he'll go mad with boredom and start making strange shapes and rambles on and on on the balcony. Interesting video though.
Awesomeness, I always love new videos of yours, they're always so exciting
+Dan Dart Thanks! They're always fun to make.
I love the lady at 5:30 who's like "Wtf is that crazy Australian dude doing?"
+1 for shading Nescafé as "a Coffee like substance" :-)
As you can no doubt deduce from what you know about the Rhombic Icosahedron, the shape made by two opposite edges and an imaginary pair of parallel lines through the Icosahedron connecting the two opposite edges is a golden rectangle.
I love polyhedrons and phi, and I literally cheered out loud when you declared that the Bilinski Rhombic Dodecahedron was made up of Golden Rhombi.
I love this stuff.
I like that person that comes into the image and is seemingly consumed by the Dodecahedron. Truly a mystery that will never be solved.
I jumped from my seat when I realized the unexpected relation to the Rhombic Triacontahedron. Really exciting video, Matt!
You deserve a million subscribers. This video was AWESOME!!!
Only curious: after your wife saw this video, are you allowed to go with her to conferences again?
Why not? He spent the whole day on maths and kept himself out of trouble.
if only kids also did the same at hotels.....
I did when I was a kid.
My countryman and a college mathematician mr. Bilinski, although I must admit I have never heard of him. Fascinating stuff, Matt. This reminds me how I once discussed one-point compactification with a matematician during a garden party and BBQ. All we neded was a ball or an orange to point at it. :-) -- -- -- --
Keep up the good work and come again soon. Greetings from Croatia.
Those magazines (and that roomservice menu) died for a worthy and highly entertaining cause! :)
I love the part when the person walks onto their balcony, looks over at Matt talking about rhombic dodecahedrons to a camera, and then immediately turns around and goes back inside.
i think i would faint if i saw prof.dr.parker asking me for scissors
Excellent piece of informative entertainment! Setting, presentation, factoids, and mathematics (geometry) are top notch. Keep up the good work!
+S .Tsing Tap Thanks! I had fun making it.
5:38 "Hey, where's our scis---oh shit, he's doing math! Hide!"
Luckily, he was doing maths, not math.
EternalBooda lolol
haha loved it! the hidden jokes in these videos are so much funnier than actual comedy videos! Thank you!
That made me so happy to see the golden ratio turn up. That's actually what I thought you were going to say about the ratio of the diagonals of the first rhombus.
this is why I love this channel
5:36 "What the fuck is he flapping his gums about now..."
These practical videos are my favorites!
omgg mat im your huge fan from croatia, cant believe you were in croatiaa, hope you had an awesome time. Judging by the hotel, you were in Dubrovnik, im from Zadar its a little farther up. Oh and btw i love physics too, i was actually 4th on the states (like the whole croatia) physics competition. love your videos byee
@standupmaths -I've been a numberphile viewer for years and have always loved your videos. Loved this one as well and keep it up; I'll keep watching. Your charismatic spin on mathematics keeps me curious (in general) and engaged in my personal betterment.
+John Fitzgerald Glad you enjoy the videos! I plan to keep on making them.
Matt! My copy of your book finally arrived. Thanks for the hypercube drawing, I think it's pretty darn awesome :D One chapter in and loving it.
+Epithemeus My pleasure! I hope you enjoy the rest of the book as well.
The golden ratio is officially a Parker square.
This is awesome. You're amazing, Matt!
Once again, I learned something about Math!!?? Matt you are amazing. I have no idea how to use this information, but I find it fascinating, and feel smarter for the experience. Thank you
+Kathryn Blodgett You never know when some dodecahedral knowledge will come in handy!
as someone who works at front desk, id be hyped as hell to lend my scissors and tape to someone constructing a rhombic dodecahedron
This is shaping up to be a be a great episode!
Wow, I was so impressed(but not surprised) when phi appeared in bilinki's dodecahedron!
Awesome video Matt! Hope you had fun in Croatia!
+Tom van de Craats I had a great time!
LUCKY!!!! Hope you're having a good time in croatia
hey that's my grandfather - thanks for the 60K views!
oh..em...gee... the point where you started using excel to divide the packet just cracked me up, this was a hillarious piece of umprvised geometry, very impressed
Awesome !!! Now I know what to do when I visit Croatia
lol, here I was googling a good visualization of the Bilinski dodecahedron while thinking about how Matt would hate it for the golden ratio, and then a video by him is the first good visualization I find. I really should just subscribe to this channel already.
How can you say the golden ratio "showed up out of nowhere" when you used it when measuring the sides?
He didn't though. He used the ratio of the side length to the individual diagonals. The diagonals weren't compared until after.
Timothy Warner Yes I know. But "showed up out of nowhere" is still inaccurate because he was using the golden ratio earlier. And since the lengths of the diagonals are intrinsically related to the lengths of the sides, there's even less of a reason to be surprised.
The reason to be surprised is that not every rhombus will be able to form a dodecahedron (in fact very few) and yet one of the rhombus'; that works happens to be in the golden ratio.
But he wasn't using the golden ratio before. If anything he was using root(4*[golden ratio]).
Clearly mock surprise... considering the formulas for the diagonals and their resemblance to the quadratic that solves to the golden ratio.
Yeeeey, Croatia :) I hope you enjoyed your stay :)
But did you show the counter staff what you made with the scissors and tape when you returned them?
+David Roberts I did not.
@@standupmaths but why? Afraid of being ashamed? Especially after all that square shenanigans?)
Best description of instant coffee i've ever heard!
I love the intro and outro music, it's so good :D
As soon as I saw sqrt(5) I had a feeling the golden ratio would be involved somehow.
+Wyatt Jackson That should have been a clear warning but I still didn't see it coming.
I enjoyed the way your neighbour popped her head out just after the 5 minute mark, and promptly went away again...and who can blame her.
Also, I hope you sent this video to the Hotel - I'm sure they'd enjoy this.
Nerdiest way to destroy a hotel room ever. I love it.
Did she lock you in? You do realize that Kings Landing is on the other side of that hill? If you need more maths to do in Dubrovnik, might I recommend you solve for Pi while you dine at Lady Pi Pi. Show her a nice time since you ruined her chances at ordering in.
When you get some more materials you can make the Subscribahedron.
Another great video, thanks for sharing. As a designer I must say this new "Rhombic" is quite interesting :)
but which one is the Parker square of rhombic dodecahedrons? I suppose it has to be the more regular since it is almost, but not quite, regular.
I am sitting here with a bag of Munchies, eating them in consistent harmony with the video. Every time Matt's voice lowers I eat one and will almost certainly be ill.
Yep, 10:19 and I am done but feeling ashamed and a little ill.
I live for Matt Parker, "A new Rhombic Dodecahedron FROM CROATIA!" The exclamation point adds great extremities of your excitement
Why is it that when you add a belt to a rhombic icosahedron you don't add 8 faces to get a rhombic octaicosahedron? Why do you need to add a 10 to get the next polyhedra in the series? Is there a larger polyhedra beyond the rhombic triacontahedron? How many faces are needed to be added to construct that one? Is there a relevant sequence in OEIS describing these relationships?
I like "I'm staying at the hotel" as validation of the craft-supplies request!
+Crap Box Photography I thought I had to say something with confidence!
Love a bit of Maths and Crafts!
why do I enjoy this so much, I'm a journalism major and can't even do basic math properly.....
I hope you enjoy your stay in our beautiful little country :)
+BSBlackSilverBoltBSB I did! It was indeed beautiful.
How do you like Croatia? Its a beautiful country and the people are super nice especially in Dalmatia.
found the hotel is in Dubrobnik, wonderful city i will hopefully go there next summer again. Also that "hat" looks like something Kryten could wear quite comfortably :D
if you give me money i can pretend to be nice and friendly as well
BaconKwagga im not talking about the hotel staff or such. I got family there and ive lived there for a while and the people are trully nice and honest. Especially in the smaller fishing villages with small communities they really know how to enjoy life
+Jan Šinkovec We had a great time in Croatia. Dubrovnik was lovely.
Jan Šinkovec Did you make a god damn Red Dwarf reference? I'm kinda very into that show right now.
Very cool! There is a great set of geometry blocks called 'Rhombo', created by Michael Longuet-Higgins (co-discoverer of some of the uniform polyhedra), the Bilinski dodec arises pretty naturally out of them, especially when you are trying to construct a triacontahedron.
+AdamLore I need to get me some of those blocks!
1:14 "How hard can this be?"
I've seen enough Top Gear to lower my expectations for a successful segment, whenever this is said.
So when does mathsgear get the rhombic d20? I just got my set of the unique polyhedral dice in the mail yesterday.
-How was the conference honey?
-It was pretty good, but it was a bit too long and I'm starving, where's the room service menu?
-Yeah well, about that...Happy Rhombic Dodecahedro day!
-You got bored didn't you?
-Yeah...
+axelarthuro123 Were you there? That is strangely accurate.
he looked so satisfied 10:56 'the croatian creation'
Very entertaining video. Keep up the good work!
matt youre so creative!
This was better than expected!
+Tiago Resende My thoughts exactly!
Is a rhombus just a Parker Square?
This is so beautiful! :'D
I see confusion when we talk about "rhombic dodecahedra" now... Perhaps we should rename the standard Rhombic Dodecahedron to something catchy & unique! From rho[mbus] + doz[en], I suggest calling it a Rhodoz!
I love so much that i found another rhombic dodecahedron enthusiast
Matt mentioned only four of the platonic solids having corresponding rhombic dodecahedra (in pairs of a solid and its dual). What about the tetrahedron? Well that is its own dual, so the resulting rhombi have both diagonals the same, and there are 6 edges on the tetrahedron giving 6 rhombuses, so the consequent rhombic hexahedron is just a cube!
His name was Stanko Bilinski and he was from Nasice, wich is in Slavonia. I am going to school in that city and every year we have a Stanko's geometry school.
Was the hotel you were staying at in Dubrovnik? I think I recognise it...
+OSR Yes it was! About 20 min walk from the old town.
standupmaths Ah! It's been a couple of years since I was last there, but it's so easy to recognise. Absolutely beautiful place.
Please tell me you ate the sugar when you were done.
5:38 can't imagine what that guy's thoughts were at the moment
🌝
it is a woman, not a guy
She disappeared almost immediately, I assume to call the authorities.
Either "Oh, someone's making a video, let's just quietly step out of the shot" or "There's a madman talking to a strange shape, let's just back away slowly..."
haha loved it! the hidden jokes in these videos make me laugh so mucb more than actual comedy videos! Thank you!
"I will definitely bring them back" - Matt
The best way to sound like he won't bring them back
You showed (among other things) rhombic dodecahedra with rhombus ratios (ratios of the two diagonals) of sqrt(2) and phi (golden ratio). Could there be other rhombic dodecahedra with other ratios that we just haven't found yet?
+Vincent Killion Maybe! I don't know if there is a proof that they don't exist.
Thanks, Matt. Good stuff as always.
+Greg Johnston Glad you enjoyed it!
I really enjoyed this video as I occasionally make polyhedra myself. However you definitely get the award for geek of the year. :-) In a beautiful part of the world and you spend the whole day cooped up in your hotel room with paper and scissors. You're in a long tradition of mathematicians ignoring their environment - in some cases like Archimedes even ignoring raging battles around them. Kudos.
The "Geek of the year awkward"?
+Declan Brennan At least I sat out on the balcony. Does that count?
Nescafe - a Parker square of a coffee. Hope you enjoyed your stay in my country - it has granted you a subscriber. :)
matt gyver, saves the world by constructing the infamous rhombic dodecahedron with sugar pacs, excell and a pair of scissors... :D
Standard people go to Croatia for vacation, mathematicians build dodecahedrons.