Guys this is much easier to make if you don't do corners! Instead, try to construct a single face and then build up from there, creating faces after faces. At first I was doing corners, and it was almost impossible. I then scrapped it all and decided to just put it together by faces, and found it much easier!
Yesterday, I watched this video for the first time. I figured I would never even attempt to make one. Today, I saw a random post-it block on my desk, and counted that there were exactly thirty notes left. Challenge accepted!
James, hats off. nice stuff. been watching you channel and numberphile for the last week like a nutcase. re-discovering the beauty of math thanks to all of these. :)
I'm surprised that nobody noticed in the comments that such a solid is not really mathematically perfect. In fact, when you calculate the angle that one can get with such folding, you'll find that the angle is not really 108 degrees, as required. In fact, it's about 108.43 degrees. The error, however, is small enough to be neglected when folding the paper.
Please try to make one with a similar design (the pentagon "cut-out" in the middle) but for an icosahedron! (triangular "cut-out" in the middle) I have high hopes that you of all people could complete this challenge!
@singingbanana you really like dodecahedra? i saw your video "how to make pop-up dodecahedron" :) it's fun to make though :) oh.. and i like your videos :) i don't get them most of the time that i have to watch it over 4 times to get it.. but very nice :)
There are lots of modular origami designs on the internet and there is definitely more than one like that. The design actually can't be very similar to this: there is someone who has invented variations of the unit where the angle between folds is 60 as opposed to 108, but the proportion of the paper makes it almost impossible to see the triangular holes. You could try a different proportion of paper and just measure the angle but that'd take some trig work. If you'd like to you can, though.
Is it necessary to take 4 units by 3 units paper? If i take a different size how will it affect the dodecahedron..Change in volume obviously or something it does like messing the whole thing..
Yes! You have to modify the angles appropriately, but you can make all sorts of solids - even ones that have more than three faces per vertex (although the model will be a bit weaker the more faces per vertex there are). I've made the cube, tetrahedron, octahedron, icosahedron, truncated cube, rhombic dodecahedron, truncated icosahedron, stella octangula, truncated tetrahedron, and many others. There are practical limits, of course. The truncated dodecahedron has such a wide angle on each module that you have to make some other modification for it to hold together (or else just glue the thing). And paper presents its own limitations on how big you can make these things before they collapse under their own weight. There's a reason people don't build skyscrapers out of paper. The module unit he presents here I first saw referred to as the "Penultimate Unit". There are many other module shapes that can be used to make various shapes, and they all have different advantages and disadvantages. I only just saw this video just now. I'll have to send him pics or vids of my own models, as he requests.
Can you get a smaller dodecahedron inside of a larger one, using enough colors that the smaller and larger ones will never correlate colors, and every face is of different colors?
@11Agamemnon235 You have an inner lattice of the 2x2 squares, and an outer lattice of the remaining 12 squares. Each move switches between the 2 lattices. There are 3x more outer lattice positions so a knights walk is not possible. Thx for the fun mental problem.
Put 3 of them together, as shown on the video, then start adding every single piece to it, making 1 side (the bottom). Continue doing this until you make another side, and another one, and eventually it will be finished. Another thing that helped me is to count the number of pieces you need to complete a side.Every side needs 5 pieces, so once you count 4, finish that side and continue. Also, once you make the 1st side (the bottom) try to expand cyclical.This prevented mine from collapsing. :)
well i may not have post-it notes but i have something i could use to make a dodecahedron, which i actually have made now XD was a pain to figure it out but i managed to do it, then eventually i wanna try making an icosadodecahedron, has pentagon sides and triangle sides. might make a video and show you if its successful :D
Correct me if I am wrong... (because I want to try it) you used 4" by 4" post-its... each corner has 3 post its... times 30 corners.. meaning I need at least 90 post it's... this might take a while but i'll email it to you soon.
@CardMagicianJoeKing I went looking online for some answers. I know each module touches 4 others, so that's the equivalent of a 4-regular graph. I found a paper that made the statement that almost all 4-regular graphs have a 3-coloring. So... Hell, i thought singingbanana's remark was a bit offhanded and that he misunderstood me. Maybe he's already worked this out?
Modular Origami I see. You should look more up and do some geometric and statistical analysis on it. Somebody did an International Baccalaureate Math Project on origami years and years ago at my school, and was one of the very few that got full marks for it.
Oh oh! There's a small graphical error. In the recap, you've made a Z to represent a cross section of the module. And if the two outer lines are 1 length unit each, the middle on is sqrt(2) length units...
i mis counted and ended up making 30 vertex units instead of 30 single modules so i had 90 modules so made 3 of them hehe does anyone know if there are ways to make any of the other platonic solids or anything like that from post-it notes as well?
There's a nice proof that there are only 5 regular solids (Platonic Solids). There have to be at least 3 faces at each corner, and the sum of the angles at each facing must be less than 360 degrees. Triangles with interior angle 60 degrees: 3*60 < 360 makes Tetrahedron 4*60 < 360 makes Octahedron 5*60 < 360 makes Icosahedron Squares, 90 degrees: 3*90 < 360 makes Cube Pentagon, 108 degrees: 3*108 < 360 makes Dodecahedron Any more facing or any larger angle and you can't make a 3D corner anymore.
I had 37mm by 50mm post it notes and I got a hexagonal pattern. It may be possible to make a hexagonal sphere but I don't know how many post it notes one needs. One post it note folded as shown gives a 140 degree internal angle and two 60 degree angles on the ends. The 140 degree angle can be used to draw a 9 sided polygon. I stapled my post it notes together but I wasted at least one staple per joint just to get it right. Maybe someone could try hot glue, super glue, epoxy, contact cement or no adhesives.
@muffemod Ah yeah, that could work well idd, less chance to let it fall apart. I was trying it with weak adhesive tape, I could peel it off after finishing the dodecahedron.
@CardMagicianJoeKing "Still can with 3 maybe" hey maybe you could. maybe... Considering the ring of colors in a pentagon, red, green, blue. It could go r-g-r-g-b. An adjacent pentagon shares two colors. so maybe r-g-b-g-b. Still... I'm not sure if you can finish it like that...
any one else having trouble putting the 3 corner sets all together? i have the moduals in there 3 part corner, and the 3 part corners in the 3 corner ses, but i cant get the 3 corner sets into the next set, anyone can help?
Hey, you should be thankful that you get regular platonic solids. My fathers brother was not so lucky, as he suffered from toroidal feces, and he never recovered from it. It's been hard on all of us, and we miss him dearly. R.I.P. Uncle loopy poop :' ((
I believe it is possible to create a 5-colour post-it note dodecahedron so that any rotation that is a symmetry corresponds to an even permutation of the colours on the top face in a way that shows an isomorphism between the icosahedral rotation group and A5. From what I could gather from the video, your 5-colour dodecahedron doesn't have that property. Considering that you are a group theorist, unless I am mistaken somewhere in this comment, I'm somewhat disappointed.
Wow, that looks very, VERY difficult. And more likely to send me into the sort of rage that I experienced the one time I attempted origami, than relieve any stress. I like the idea of the multicolour one though...
Guys this is much easier to make if you don't do corners! Instead, try to construct a single face and then build up from there, creating faces after faces. At first I was doing corners, and it was almost impossible. I then scrapped it all and decided to just put it together by faces, and found it much easier!
Wow James, this is really cool...
This video is very concise, and clearly illustrated. I had no trouble building this (aside from those last few pieces, ha!). Thanks for this video!
I just finished mine! It took forever to get started, but it was pretty simple once I figured everything out. Thanks so much for the idea!
I made one, it is so fun and my parents and my brother were amazed. Thanks so much singingbanana! :)
Yesterday, I watched this video for the first time. I figured I would never even attempt to make one. Today, I saw a random post-it block on my desk, and counted that there were exactly thirty notes left.
Challenge accepted!
Using the same 4 by 3 piece of paper, you can also make square, hexagonal and triangular modules too.
James, hats off. nice stuff. been watching you channel and numberphile for the last week like a nutcase. re-discovering the beauty of math thanks to all of these. :)
@swinjy You need to double that (an edge has a corner at each end), there are 20 corners.
How many of those units do you need to make and then do you just put those corners together to make it?
I'm surprised that nobody noticed in the comments that such a solid is not really mathematically perfect. In fact, when you calculate the angle that one can get with such folding, you'll find that the angle is not really 108 degrees, as required. In fact, it's about 108.43 degrees. The error, however, is small enough to be neglected when folding the paper.
Please try to make one with a similar design (the pentagon "cut-out" in the middle) but for an icosahedron! (triangular "cut-out" in the middle) I have high hopes that you of all people could complete this challenge!
Santa brought me here to make baubles for my cylindrical Christmas tree.
@Gameboygenius I actually was aware of that, but decided the diagram would be clearer if I made it that way :)
@singingbanana you really like dodecahedra? i saw your video "how to make pop-up dodecahedron" :) it's fun to make though :) oh.. and i like your videos :) i don't get them most of the time that i have to watch it over 4 times to get it.. but very nice :)
There are lots of modular origami designs on the internet and there is definitely more than one like that.
The design actually can't be very similar to this: there is someone who has invented variations of the unit where the angle between folds is 60 as opposed to 108, but the proportion of the paper makes it almost impossible to see the triangular holes. You could try a different proportion of paper and just measure the angle but that'd take some trig work. If you'd like to you can, though.
I love how you call your wee bit o' paper a module. :)
Nice model! I wish I'd seen this video two years ago, when i first started doing modular origami.
Is it necessary to take 4 units by 3 units paper? If i take a different size how will it affect the dodecahedron..Change in volume obviously or something it does like messing the whole thing..
Of course! Nice.
I like how you get so excited about that. Thank you
hey singingbanana, just completed mine! took a bit of fidgiting with the modules to fit together at the end, but that was FUN to do!!!
This is so cool! I'm definitely going to try this out
Can one make any regular solid with 3 faces per vertex, like a tetrahetron and cube?
To the stationary store!
Yes! You have to modify the angles appropriately, but you can make all sorts of solids - even ones that have more than three faces per vertex (although the model will be a bit weaker the more faces per vertex there are). I've made the cube, tetrahedron, octahedron, icosahedron, truncated cube, rhombic dodecahedron, truncated icosahedron, stella octangula, truncated tetrahedron, and many others. There are practical limits, of course. The truncated dodecahedron has such a wide angle on each module that you have to make some other modification for it to hold together (or else just glue the thing). And paper presents its own limitations on how big you can make these things before they collapse under their own weight. There's a reason people don't build skyscrapers out of paper.
The module unit he presents here I first saw referred to as the "Penultimate Unit". There are many other module shapes that can be used to make various shapes, and they all have different advantages and disadvantages.
I only just saw this video just now. I'll have to send him pics or vids of my own models, as he requests.
If the multi-coloured one gave you headaches, you should try to build the five intersecting tetraedra. You can find it somewhere around on youtube.
@wrightmath Yup.
Are there any other shapes that can be made from a similar repeating module?
Can you get a smaller dodecahedron inside of a larger one, using enough colors that the smaller and larger ones will never correlate colors, and every face is of different colors?
@11Agamemnon235 You have an inner lattice of the 2x2 squares, and an outer lattice of the remaining 12 squares. Each move switches between the 2 lattices. There are 3x more outer lattice positions so a knights walk is not possible.
Thx for the fun mental problem.
@lmcgregoruk Yes you did.
Put 3 of them together, as shown on the video, then start adding every single piece to it, making 1 side (the bottom). Continue doing this until you make another side, and another one, and eventually it will be finished.
Another thing that helped me is to count the number of pieces you need to complete a side.Every side needs 5 pieces, so once you count 4, finish that side and continue.
Also, once you make the 1st side (the bottom) try to expand cyclical.This prevented mine from collapsing. :)
This guy really needs more views! He is a boss
Wait.... thirty corners or thirty modular individual pieces...?
Yeah, ive replaced basically all of my subscriptions with various youtube educators and vloggers, amazing how much can change in 9 months.
How do you connect the corners? My math teacher is making us do this but I am a little confused.
I shall attempt this. But I cannot help myself, and ask... isn't the plural 'dodecahedra'?
Modular Origami - Best use for spare time and paper :D Do you know Sara Adams?
well i may not have post-it notes but i have something i could use to make a dodecahedron, which i actually have made now XD was a pain to figure it out but i managed to do it, then eventually i wanna try making an icosadodecahedron, has pentagon sides and triangle sides. might make a video and show you if its successful :D
2:54 - Damn it, Grime! Why are you working for Abstergo?
Do you still check that email address?
Correct me if I am wrong... (because I want to try it) you used 4" by 4" post-its... each corner has 3 post its... times 30 corners.. meaning I need at least 90 post it's... this might take a while but i'll email it to you soon.
I want to know how to make a regular pentagonal bipyramid, the Pluto of the Platonic solids.
Exactly! It's easy to think each would fit into a category, but a little thought reveals they don't quite belong.
@CardMagicianJoeKing I went looking online for some answers. I know each module touches 4 others, so that's the equivalent of a 4-regular graph. I found a paper that made the statement that almost all 4-regular graphs have a 3-coloring. So... Hell, i thought singingbanana's remark was a bit offhanded and that he misunderstood me. Maybe he's already worked this out?
Can you make a 3 color dodecahedron with no same colors touching? I must try that.
Lovely. First origami thing I've seen that made sense. ;^) Thank you.
Modular Origami I see. You should look more up and do some geometric and statistical analysis on it.
Somebody did an International Baccalaureate Math Project on origami years and years ago at my school, and was one of the very few that got full marks for it.
Great idea, thank you soooo much. My math teacher is really amazed and happy when I give him origami/post-it note pieces similar to the dodecahedron.
@oEQjet You can...
and of course I have to see this clip during my finals.
Well the orange dodecahedron surely looks nice in my room. Thx
How do you have five different colors?
Oh oh! There's a small graphical error. In the recap, you've made a Z to represent a cross section of the module. And if the two outer lines are 1 length unit each, the middle on is sqrt(2) length units...
can you use a full pice of papper?
i mis counted and ended up making 30 vertex units instead of 30 single modules so i had 90 modules so made 3 of them hehe
does anyone know if there are ways to make any of the other platonic solids or anything like that from post-it notes as well?
When British children sing their ABCs, do they say "zee" or "zed"??
There's a nice proof that there are only 5 regular solids (Platonic Solids). There have to be at least 3 faces at each corner, and the sum of the angles at each facing must be less than 360 degrees.
Triangles with interior angle 60 degrees:
3*60 < 360 makes Tetrahedron
4*60 < 360 makes Octahedron
5*60 < 360 makes Icosahedron
Squares, 90 degrees:
3*90 < 360 makes Cube
Pentagon, 108 degrees:
3*108 < 360 makes Dodecahedron
Any more facing or any larger angle and you can't make a 3D corner anymore.
Awesome! I'm going to try that when I come home.
@427557 You don't make ten 3-piece units. Instead you make a few (I made three 3-piece units) and laced a bunch of individual modules to make it.
Can teach us how to make a great stellated dodecahedron as well?
@muffemod I watched the video on your channel and I was wondering the same, I was also having trouble getting the compounds together. :S
Can you please tell us how to put the modules together!!!!!!!!!!!!!!!!!!
I had 37mm by 50mm post it notes and I got a hexagonal pattern. It may be possible to make a hexagonal sphere but I don't know how many post it notes one needs. One post it note folded as shown gives a 140 degree internal angle and two 60 degree angles on the ends. The 140 degree angle can be used to draw a 9 sided polygon. I stapled my post it notes together but I wasted at least one staple per joint just to get it right. Maybe someone could try hot glue, super glue, epoxy, contact cement or no adhesives.
30 modules or corners?
Satyajit Das modules
Brilliant. I know what I'm making at work tomorrow!
how to piece together all the corners? plz help me
@muffemod Ah yeah, that could work well idd, less chance to let it fall apart. I was trying it with weak adhesive tape, I could peel it off after finishing the dodecahedron.
This was easy to make, but it looks awesome!!! Thanks!
@CardMagicianJoeKing you're confused, think of the left side as the top, and the right side as the bottom (flip it 90 degree's right)
This is BRILLIANT.
So wait how much modules? 30, 60, or 90??
derpy chez 30
Interesting- now that's a good permutation-combination problem there- plus you're solving a problem while making something. Sounds fun!
watching this 1 am is really hilarious, made me go and find post-its :)
@CardMagicianJoeKing "Still can with 3 maybe" hey maybe you could. maybe...
Considering the ring of colors in a pentagon, red, green, blue. It could go r-g-r-g-b. An adjacent pentagon shares two colors. so maybe r-g-b-g-b. Still... I'm not sure if you can finish it like that...
any one else having trouble putting the 3 corner sets all together? i have the moduals in there 3 part corner, and the 3 part corners in the 3 corner ses, but i cant get the 3 corner sets into the next set, anyone can help?
90 post it notes total?
Great Video. I'm gonna have to teach this to my club ^.^
So you need 90 post its?
This man draws the straightest lines I've ever seen, WITH A PEN.
Love it! I'll make one in the weekend :D
Hey, you should be thankful that you get regular platonic solids. My fathers brother was not so lucky, as he suffered from toroidal feces, and he never recovered from it. It's been hard on all of us, and we miss him dearly.
R.I.P. Uncle loopy poop :' ((
i dont get how to connect the three modules to eachother
Success! It took about two hours, but it was definitely worth it.
I need all the friends I can get.
"Oh yeah I want to do this it seems like fun and I can show everyone my epic skills" *Checks upload date* "Oh."
This is hilarious now
@GallifreyGames Ya i know, i just love hearing people say it like that.
@superfluousness321 I love how you call his module a wee bit o' paper
This is a great but incomplete video; please include instructions on how to put the modules together.
He did, the same way you put the corners together, you add 2 more to the other ends.
I made one too! Looks awesome. 15 hours later my fingers are still in pain but #YOLO, right? :-D
I'm currently making one. I'll probably send you a video response :3
How to connect
@javalin597 Pretty sure I heard him on Chris Evans Breakfast show on Radio 2 at work this morning, as the 3 minute mystery interview.
@killeramaru you need only 30 post its. 30 modules... not 30 corners
Now I have use for my colourful post it notes =D
i'm so glad i have post-its. i'm gonna make one
I wish I knew more super math teachers on youtube ): do you know any similar to yourself?
that's great - I'm going to make one at work :D
Took me three hours, but I did it!!!
wow i'm impressed! do u want to be my boyfriend?
@@leamusic50 thanks and ok but you have to make one too
THAT IS SO COOOOOOL!!!!!
I believe it is possible to create a 5-colour post-it note dodecahedron so that any rotation that is a symmetry corresponds to an even permutation of the colours on the top face in a way that shows an isomorphism between the icosahedral rotation group and A5. From what I could gather from the video, your 5-colour dodecahedron doesn't have that property. Considering that you are a group theorist, unless I am mistaken somewhere in this comment, I'm somewhat disappointed.
Wow, that looks very, VERY difficult. And more likely to send me into the sort of rage that I experienced the one time I attempted origami, than relieve any stress. I like the idea of the multicolour one though...
@HappyMemoryXD Nice.
after he said how much I needed to had I started laughing like an idiot nervously :{)