I liked how the macro camera scaled down your hands ;)

@standupmaths

7 жыл бұрын

+schogaia That's the quality you get from a top-end macro camera.

@andrewxc1335

6 жыл бұрын

7:04 - And the "mouth mute" button must be handy, preventing your mouth from becoming a distraction when viewing the "macro" mode. Only the best for this channel!

@sadiquehaque3460

6 жыл бұрын

schogaia I thought his hands were shrinking 😂

@noob-sniper1131

6 жыл бұрын

schogaia me too, I was wondering how that possible?

@noob-sniper1131

6 жыл бұрын

You see how big the pen looks

"It's a square so you can fold it in half whichever way you want." *folds it diagonally*

@TheRealJavahead

7 жыл бұрын

trejkaz yes... or infinitely many other ways, if you don't over define what half is (as hasn't been done here) as long as the fold passes through the Centre of the paper.

@U014B

3 жыл бұрын

Wait, that's illegal

13:59 Lol the giant yellow pencil. I love your dedication.

@BakerB

7 жыл бұрын

*dodedication

I don't know what's funnier, the "macro" camera gag, or the fact that so many people are so confused and don't understand what's happening haha XD

@ffggddss

7 жыл бұрын

Yeah, it's a wonderful invention that magnifies only inanimate objects, like the paper squares; not animate ones, like Matt's hands. I don't know how that escapes so many people.

@SquintyGears

7 жыл бұрын

it's because the editing is so well done XD it's great

@callratchet2295

7 жыл бұрын

D. C. Lol I know first I see he holds the paper with his fingers and next clip he holds the paper with his wole hand Lol I was like o.o all the time

@Dooge

7 жыл бұрын

it got me the first time, but once I saw his hands were tiny compared to the second dodecahedron shot I realized that I had been gaffed, but at least not all the way through the video, I find it hilarious.

@DavidDMD1991

7 жыл бұрын

Or the table.

Loving the macro camera! Haha.

@standupmaths

7 жыл бұрын

+Enzo Grispo It's cutting-edge close-up technology.

@tpat90

7 жыл бұрын

Well played, Mr. Parker. Well played. PS: My reaction at "0:20": 'No, you don't, your hands are still in scale and not skewed to hell and beyond.'

@TheNefari

7 жыл бұрын

More than the actual origami dodecoration to be honest :D

@MalcolmParsons

7 жыл бұрын

I love the pen close-up.

@nrellis666

7 жыл бұрын

especially the way it makes the dodecahedron look bigger and Matt's hands look smaller

I tried doing this but I can't get the paper to change size =/

@IndigoGollum

2 жыл бұрын

Maybe you need a higher end zoom camera.

Really like your zoom-macro solution. I gotta say it's genius, no, GINORMOUS.

Man, you can make anything look bigger with different angle and lens!

@bad.art.bymaria

7 жыл бұрын

I think that the paper was actually bigger, considering the relationship to a hand :)

@devon5714

6 жыл бұрын

Yeah, everything except Matt's hands. :P

Wow, the close ups... just amazing. Standupmaths really is at the pinnacle of Macro Lens technology!

watching stand up maths: 1) yah, i know 2) yah, i know 3) yah, i know 4) oooh, that's cool 5) *jaw drops*

Hi Matt! I was actually playing with this a few weeks ago. It turns out the symmetry group (all the rotations) of the dodecahedron is the same group (isomorphic) as the "Alternating group on five letters" (A5) - which is taking a list of 5 things i.e. {red, yellow, blue, green, white} and swapping one element for another an even number of times. i.e. {yellow, red, blue, white, green} is another element under this rule (2 swaps - 1st,2nd and 4th,5th - OK). but {yellow,red,blue,green,white} isn't (1 swap - 1st,2nd - Not OK). All the other even number of swaps you can do will be elements of this group. And now, if you look at any pentagon face (in one of it's 5 orientations) - the order of the colours of the edges (count them going round clockwise, from the bottom edge) will be elements of the group. This also means rotating about one of the pentagons is a group operation, i.e. {red, yellow, blue, green, white} -> {yellow, blue, green, white, red} Another operation you can do is rotate around a vertex, which will permute three of the colours. (e.g. 1st, 3rd,5th) -> {blue, yellow, white, green, red} With these two operations, you will be able to get to any other orientation of the dodecoration (they are the generators of the group) So you're right that any single swaps don't appear, as they are elements of the larger group, which allows for both even and odd swaps ("symmetric group" - S5) - but the dodecahedron rotations only allows you to do even swaps. If you do a single 'odd' swap on the list of colours, and then only do even swaps afterwards, you'll have an odd swap in total. So if you build the dodecahedron out the 'missing' pieces, it won't share any of the face colourings of the original.

@JensGulin

6 жыл бұрын

The descriptions says there is still no answer to the coloring question, but I scanned the comments and suggest that everyone "like" this thread to get it higher for those looking for it. Coloring the edges are equivalent to coloring the faces of a rhombic triacontahedron www.mi.sanu.ac.rs/vismath/zefiro/_polyhedra_colouring_2007_08_10.html#Rhombic%20triacontahedron www.georgehart.com/virtual-polyhedra/five-cube-intersection.html They say there that it's only possible to color it one way. Either that's wrong or you would find that the two color schemes found are actually one and the same, just differing in the mapping of color to each letter. Haven't verified myself, but there is actually a different suggestion below, found if you're not blinded by symmetry. Contradicion, yes here they seem to make sure to avoid mirror faces and find another color scheme. kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12ry51hululc5c3y22wi5q5ommqhhini Explaining the colors Matt found and missed however relies on a symmetric choice. Best explanation, I think, is this thread based on group theory kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12izlsqak22innxp04cj3goskvqwlyavnc0k but these say the same kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z131tpkorlz5cvm5m04cftvw1wbmex1qkfw kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12hdt2yfrewz5hw104cirjw3uvkjfn4v1g kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12kyx1jfxrxfvbta22hfnmz2ujetxwjl04 kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12iuzaimvenvx50f233tbkpcxnoxrusw kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12zvjoiiun1hp2ur23dc1artzvkzjilm kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12kzlazytqainumu23gyzjwsy2ie5aef kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z13ewn0omp32w5zll222jnvqptahvfstj kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z13msz1zvpeyexmk523wynebjkivvn01s and it's also the property mentioned in the video. kzread.info/dash/bejne/hopr1cSalsnbftI.htmlm12s Some point at the vertices and chirality kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z13li5baeve4c5lii04cc3jrnojoxzabvzw0k kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12cw1k4uxyqxfxgi04ce3cwjv3bz5yizsw0k other focus on geometrics and mirror faces to find same conclusion. kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z13ecnopsvyrcf5ht04ci35aqruzzzwyqn00k kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12ijn0yvrr0x5euc23mxrwxeny2ddfl5 kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z130xdibznmkcj1km223c5tqvsu2e3sbd04 kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12bu15gnzb5fxent23jvnih0om5v1t1i kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z120hzeapnv3s15ic04cinxibq2guhersxo0k kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z135fv3gtwnyzpdec22efz5awt2edfj02 Bonus mention for additional math that is worth looking at. kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z121sjpwdseagd0qz04cj1v4nyrqijn5kto0k kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z133ypbzzqbctjxsh23luxy5xwzsupnxc04 kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z13csfbiwrzpipcvq23hvnuy4kzszfth504 kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12dz3j5toqkgjlhk04cjrnp1kjbvd0gq14

@Scigatt

4 жыл бұрын

@@JensGulin The picture in kzread.info/dash/bejne/hopr1cSalsnbftI.html&lc=z12ry51hululc5c3y22wi5q5ommqhhini does not work anymore. I believe at i.imgur.com/9zS6kWW.png is a colouring that avoids mirror faces. Also look at pastebin.com/tk2nBeLu for a write up I did.

That opening joke almost made me spit out my tea. Well done, Mr. Parker, for that Parker square of a pun. :p

Love the macro lens. Somehow your hands aren't affected ;-)

@astropgn

7 жыл бұрын

It is the angle. He is a mathematician, so he knows how to fool our perspective

@bloodhiybrid

7 жыл бұрын

Marcos Vinícius Petri no he just used bigger objects... there is no angle that changes the size of things that drastically

@astropgn

7 жыл бұрын

bloodhiybrid Man, don't be a party pooper. I know this. He obviously used two sizes of paper and made two objects of different sizes. We are all just getting into the fantasy.

@iismitch55

7 жыл бұрын

He also used a giant fountain pen lol.

@astropgn

7 жыл бұрын

OMG, I died now!! I hadn't watch that part, thanks!

Dude, its killing me that the macro shots use large paper than the regular shots. That confused the hell out of me for the first couple minutes.

@Scy

7 жыл бұрын

He also has huge identical pens and pencils for those shots. Cannot unsee.

@Racanithu1

7 жыл бұрын

If you look closely enough it's not a micro shot. He just made a 2nd one but then about 2x larger. You can see that at 6:16 When the larger one he is making is the scale of his table. :D

@martinshoosterman

7 жыл бұрын

Scy nah, those were just funny tbh, thanks to their stubby writing ends it helped make the larger version look clearly distinct from the smaller version, letting me enjoy the humour. :P

@soupy4099

7 жыл бұрын

the best is when he has a giant version of the pen

@stylis666

7 жыл бұрын

You'd think that people who watch this channel appreciate angles...

We can always count on you to take the sight gags to the next dimension on your videos - absolutely loved the macro bit.

Instruction not clear enough; I made a hyperdodecahedron.

@joshid

7 жыл бұрын

Topsoil Depletion Awareness haha most other people won't understand this

@franzschubert4480

7 жыл бұрын

I think on a channel like this many people should understand what it is.

@belg4mit

7 жыл бұрын

Absolutely, there were imprecise. I folded in half diagonally and ended up with a rhombic dodecahedron.

@wintersummers3085

7 жыл бұрын

Instructions not clear; penis caught in ceiling fan.

@SomeRandomFellow

7 жыл бұрын

Topsoil Depletion Awareness hyperdodecaration

For anyone wondering why this works, the obtuse angle he made when folding it like that at 3:15 turns out to be about 108.4°, which is only about 0.23% away from the 108° angle of a regular pentagon. A slight drawback is that these little errors do eventually rack up and the vertices of the dodecahedron have little holes in them.

The "Macro Cam" was brilliant. The totally normal sized pen was what sold me on it, hilarious stuff.

If you swap two colours throughout the 5-coloured dodecahedron you made, you will obviously still have a dodecahedron with a valid 5-colouring. Every face will have exactly 2 colours swapped by construction. So there are two ways of 5-colouring it - one containing all even permutations of the 5 colours, and one with all the odd permutations. What is even more interesting is that rotating a 5-coloured dodecahedron is equivalent to permuting the colours - by an even permutation cause otherwise you get the other one. There are 60 even permutations of the 5 colours, corresponding exactly to the 60 rotations of the dodecahedron.

@bobthegiraffemonkey

7 жыл бұрын

Was going to explain this myself, but I checked first to see if any comments had already explained it better than I would. I knew I found one just by recognising the username :)

Matt doesn't have a macro lens -- he just made giant versions of everything.

@markcox5385

7 жыл бұрын

Shh! Don't spoil it for the kids! ;-)

I love the macro camera! I hope you use it more often. It really helped me to see the detail.

On the 5-colored version each color of edges basically makes a cube - if you look at, say, all the white edges they line up exactly with the faces of a cube. This is true of all the colors

I made five of these a few years ago after watching a James Grime video, all out of post-it notes. I did one with one color, one with two, one with three, one with five, and one with six colors. I made a plan to do all the other factors of 30, but then I realized I would need a lot more colors of post-it notes and then I got bored and did something else.

The giant yellow colored pencil is my favorite thing XD

If I ever end up in government I'm making this guy official secretary of math

@SomeRandomFellow

7 жыл бұрын

senororlando2 i would too even though im american

@senororlando2

7 жыл бұрын

Some Random Fellow me too, in the commonwealth I think it'd be Maths

@PineaFan

6 жыл бұрын

The chief executive decorative mathematician

Lovely! Perhaps next time you do origami you could try a stellated dodecahedron, or maybe a tetrahedron like the Five Intersecting Tetrahedra.

The fact that Matt has a giant yellow pencil is the best of the video

love the sneaky scale changes

There's somthing about a macro camera that you just cant beat!

I'm so happy you did this! I made so many very recently. My friends and I even made a snowman with dodecahedra of decreasing sizes!

Cried when I saw the huge yellow pencil. Entertainment factor is off the chart

I love that he smiled at his own use of the over sized colored pencil.

Thank god (or Matt), finally something to watch during these boring days.

@standupmaths

7 жыл бұрын

+Pav Phone I'll take that credit. :]

"and I have a macro scale camera..." Oh god. I didn't notice on the first and second transitions to the macro camera. But when I did it gave me such a giggle. Well played.

indeed, the faces on the five colored one appear to be even permutations of an original face (as in, an even number of edge swaps). This is supported by the opposite faces, because they are sequences of length 5 (which is odd), the reverse of the sequence is an even permutation of the original.

I just found this in my watch later where is has been lurking for 11 months. Much to my surprise it contained an amazing macro photography effect! Well done.

I wish I could add an extra like for the macro cam, such a casual (but awesome) use of the jumbo-sized coloured-pencils and multi-coloured pen! :)

The fact you bought an huge yellow pencil makes the "macro" cemare so much better. To bad you didn't buy yourself a huge table and a set of huge foam hands.

I believe the reason that the opposite faces wind up mirrors instead of the other 6 combinations is because of the same properties that cause the opposite vertices to be mirrors. For example, I happen to have the video paused at 17:46 and I can see the Yellow-Green-White vertex facing me, and through the whole directly under it I can see the opposite vertex as well. And I can see that the face with the white and green sides of that vertex (top-right of that vertex), is opposite of the face with the white and green edges of the opposite vertex as well. So continuing this pattern around means that each opposite face is forced to be a mirror, so you wind up with 6 combinations and their mirrors.

Notice how the centers of every edge group of some color forms the centers of the 6 sides of a cube (or the 6 vertices of an octahedron), this shows how the symmetry of a dodecahedron relates to the symmetry of a cube. cool stuff!

13:59 should be the thumbnail for this video. Hilarious! And how is Matt not cracking up laughing at 14:01? He plays it ALMOST straight-faced.

As for why you only get half of the possible sets of 5, it's a bit of group theory. The symmetry group is A5, the even permutations on 5 points, which are here represented as the 5 colors. Note that, with the nice way you've placed the 5 colors, any way you move the dodecoration you are permuting some or all of the colors. Since the symmetry group is only even permutations, you can't have a single transposition, which would be odd. Yet you need a transposition to get from some of the sets of 5 to the others. In other words, there are two conjugacy classes of elements of order 5.

The consistency between the normal and macro camera is great! Who would've guessed that optic physics can be trusted? :P

I loved the macro cam and its marvelous magnifying features.

usually i wait for a really funny part in a video before i give it a thumbs up. 8 seconds - "dodecoration" must be a new record! gj, matt!

gotta love that macro cam, and matt's cheeky grin x

The change in perspective to the larger items was blowing my mind the entire time.

i was really expecting "first of all, last christmas, i gave you my heart"

If you use 6 colors, you can place the colors in a way that makes the dodecoration look like 6 intersecting rings, each of one color.

the macro shots are great, very slick

origami on standupmaths? hell yeah!

"I'm not gonna buy that the paper at 2:03 is the same of the one at 2:06" A few minutes later (13:49): "Oh c'mon!"

Loving the comments about the macro bits. Great idea Matt!

i love the "macro" camera, I haven't seen it done the way you did it before

i have used a similar module to make a few different shapes. the dodecahedron is one of the smallest. the one most people like most is the torus,10 heptagons all connected in a line to form the inner ring, hexagons to fill space, and 10 pentagons along the outer edge to curve in the surface. it can be done with just 5 but then it loses its roundness similar to how the buckyball(90 pieces) is much more round than the dodecahedron

The timing with the cut to the parallel larger version is just surreal 😂😂 top quality visual effect and it looks hilarious

@samanpradeep3168

4 жыл бұрын

Asabyavideo

You know when matts playing a prank, he smorks his way through the whole video!

@yastay2839

7 жыл бұрын

Smirks* it's a word apple I swear!

I love the "macro" camera. ;D

Your channel brings me so much joy. And I'm still recovering from seeing that giant yellow pencil in your macro cam. Truly a stroke of genius. Thank you.

Maybe the 6 permutations of colours on the pentagons are the even permuatations, and the other 6 not on there are the odd permutations? If that's the case then swapping two of the colours should give you all of the other permutations.

This macro camera thing is trippin' me out.

I was watching this video with my nephew, who does not speak English but was interested in the origami side of it. So I muted the sound, it's very funny to watch you with no sound!

Woah, you really align with my nerdy interest, cubing, origami.

The "macro" pen really impressed me. Thanks Mat

bought your book! loving it already!

My favorite thing about this video is how the "macro close-up camera" is actually just him folding massive squares of paper on a separate video

Love the scaling you used. Definitely gotta try to build one of these

that macro camera has some interesting properties :P

The Best Macro Ever!

I'm in love with the macro came, keep using it, Also Great channel (one of my favourites ) I mean the way you present Maths, origami as in this video or everything else is great, keep up, just please try to increase your viewer interactions, anyway love your channel, great work.

I made about ten of these as centerpieces for an event and have become really familiar with the method. I was therefore very excited to find that Matt had a tutorial on the exact same design.

The editing on this video is brilliant!

I think it has to do with the "parity" of the different pentagon colourings. So there are 120 different permutations of the five colours, but there are only 24 essentially different permutations because of rotation. If you count the mirror image, there are only 12. Both rotation and reflection are "even" permutations, because you have to do an even number of switches to rotate or reflect with 5 colours. So of the 12 different permutations of the pentagon colouring, 6 of them have one parity, and 6 of them have the other parity. That is why there were only 6 different colourings on your dodecahedron (up to rotations and reflections). I'm not exactly sure if you can make a dodecahedron with all 12 permutations, something tells me it might be impossible...

Y'see... Now that I'm looking at it... I think, and stick with me here, the macro shots MIGHT actually be just bigger pieces of paper.

@standupmaths

7 жыл бұрын

+xXjesperoXx I don't understand what you're trying to say.

@KenPower1

7 жыл бұрын

No, it's one of those new 'reverse perspective' macro lenses,, The hands (nearer the camera) are projected onto a smaller area than the paper. something to do with non-euclidian geometry, I'm sure +Standupmaths can explain, maybe do a video about it?

lovin' your close up camera

I love how matt shrunk to do the close up shots

All colourings of the pentagrams are even permutations among each other, that means, you get from one pentagram with an even number of transpositions to any other pentagram, but no odd permutations are on the dodecahedron. The even permutations are a subgroup from all permutations.

Regarding not all 12 cycles of 5 colours appearing in the 5-edge-colouring, this is because of a few things combined: 1) For each colour, the six edges of that colour lie on the faces of a cube, 2) If a rotation of the dodecahedron leaves a blue edge where a red one used to be, then all six blue edges end up where all six red edges used to be, so each rotational symmetry of the dodecahedron naturally results in a permutation of the five colours. 3) No non-trivial rotation leaves three of these cubes where they are, and the trivial rotation leaves all five where they are, so no rotation merely swaps two cubes. 4) If a cycle ABCDE appears in the edge-colouring, BACDE can't also appear, otherwise the rotation mapping the ABCDE face to the BACDE face would contradict #3. This embedding of five cubes in a dodecahedron is a nice visual proof that the group of rotational symmetries of the dodecahedron is A5, the alternating group on 5 letters (or 5 colours). "Alternating" in this context means you can't swap two and leave the rest fixed.

that editing was so perfect, i was so confused at first. congrats, it was amazing

You had WAY too much fun with that macro camera

I am confused by how the graph helps with the origami but love this video...the giant pens threw me for a second. Haha well done!

where can you get those giant pens and pencils? They would be fun

Matt, can I just say that your 'macro' lens was great to watch. Loved this video.

That macro lens is pretty sweet.

I see what you did there Mr Parker, Bravo!

Hey Matt, I got your book for christmas. It's awesome!

It makes sense that you can't have all 12 combinations of faces as the graph for the dodecahedron only had 6 faces, with it being flipped when you look from the "bottom". Same reason it works for the corners, rather than thinking of the 3d object it may be clearer to look for the face/edge/vertex patterns through the graph

If memory serves (it's been a few years since I worked closely with this sort of thing), the edge colouring of the faces and why you get 6 of the 12 possible plus their mirror images has to do with the symmetry of the shape. One way to visualize what's happening is to cut the dodecahedron along the plane between two opposing faces and flip one half over to overlay the other half. Another way to consider it is that once you pick the first face's colouring, you've automatically restricted the possible colourings of the adjacent faces because of the restriction of 5-coloured faces and 3-coloured vertices (eg: a blue-green corner of a face means the third edge on that vertex only has 3 possible colourings - red, white, or yellow). As you continue to fill those faces under the given restriction, you find that eventually you're forced into using the mirror images of the original 6 faces rather than continuing to exhaust all 12. I know this isn't a rigorous proof, but it's hopefully enough to get you on the right track to seeing why it works. If I have a chance later, I'll try to work out a full proof and provide it for you.

@DrGerbils

7 жыл бұрын

Unless I am mistaken, and I've gone cross-eyed double checking it, I have found a coloring using all 12 permutations. See plus.google.com/u/0/b/105076799072526075058/photos/photo/105076799072526075058/6368669072548148978?icm=false Sorry about the two shades of green. They looked better in Paint.

@mestiarcanus

7 жыл бұрын

So I was working out some constructions (starting with a symmetric construction which generated Matt's colouring) to better understand what was going on before moving into the group theory. I came across the same one you have when I realized that my first intuition when I made my original post was forgetting a degree of freedom. Of note, this colouring has some permutations at the vertices which are duplicated, so it uses 14 permutations once and 3 twice, leaving 3 unused. For example, the right-most outer pentagon vertex (red - light green - purple) has the same colouring as the left-most inner pentagon vertex. The three pairs are also located opposite each other on the dodecahedron (that is, at pairs of vertices which are farthest apart on opposite faces). Now that I've built up some more intuition I'm working on the group theory behind all this. Since it's possible to consider each face as a permutation of four elements (ie: number the colours and enumerate the edges of a face, starting with the position labelled 1 so edges 2-5 are permuted), this looks like a subset of S(4) - possibly even a subgroup. I'm currently taking the colouring Matt posted and the colouring you posted and looking at the groups they represent to work out the generators and see if I can come up with a complete proof of the possible colourings. I'll come back in a day or two once I've (hopefully) worked it out but this is a particularly busy week for me both at work and home so time is limited (and bouncy buses aren't very conducive to writing much during my commute). Hopefully I can find out if it's possible (or why not) to colour using 12 non-mirrored faces while still using all 20 vertices, or some other nice constructions, and why we lost 3 vertices to double another 3 when we made our construction.

@DrGerbils

7 жыл бұрын

mestiarcanus Here's a coloring I made directly. The previous one was the result of recursive edge swapping. It too has at least 3 duplicated vertex patterns. This coloring resulting from starting with Matt's coloring and swapping 3 pairs of edges, specifically the grey and purple in the outer pentagon, the grey and purple edges that connect the outer pentagon to the decagon and the uppermost grey and purple edges in the decagon. I see now that each of those swaps created a duplicate vertex coloration pattern. plus.google.com/u/0/b/105076799072526075058/photos/photo/105076799072526075058/6368716594148316578?icm=false&authkey=CIG9ycXK_PLNLA&pageId=105076799072526075058

@mestiarcanus

7 жыл бұрын

The edge swapping is actually how I had made my non-Parker colouring (or is this the Parker colouring because it doesn't use all the vertices). I found that by enforcing 3-colouring of vertices and 5-colouring of faces, once I made one edge pair swap it forced the rest and I suddenly had the 12 unique face colourings.

so there ARE perks to staying up till 5:22AM for me

@standupmaths

7 жыл бұрын

+Relish Relisher It's a civilised 13:22 here.

@Ienjoylotsofstuff

7 жыл бұрын

damn you timezones!

@jacobp.2753

7 жыл бұрын

Relish Relisher when you try to say a time and it turns into a time stamp

@turun_ambartanen

7 жыл бұрын

Whatsapp makes me so angry with it's number highlighting. it's totally unnecessary!

I love this sort of practical video! This and the hexastix are awesome! Would love it if you could do more videos along these lines! :)

If you number the colors 0, 1, 2, 3, and 4, and then write down the numbers around a face (starting at zero) you'll get the even permutations of the numbers 1 to 4 (or odd, based on how you number them).

As a compsci guy I love the lists starting from 0, makes me smile everytime.

love the camera work

I haven’t scanned all 723 comments but it occurred to me that, as I haven’t any square paper, could I use any rectangular shaped such as a sheet of A4? Then I though about the geometry, which lead me to calculate the angle created by the folding. I used GEOMETRY, which is a branch of maths as I was taught, back in the old days. It turns out that the angle created by the folding, is 108.44 deg, which is so close to the ideal of 108.0 deg, that I thought it extremely clever. I found a drawing construction for a pentagon many years ago, back in the 70’s, and it astonishes me even to this day.

Your close up thing reminds me of this Aussie children's show that was on when I was a kid, called Johnson and Friends. All the proportions were slightly off and it made me feel strange and uneasy when I watched it but I didn't know why. I figured out, when I was older, it was because it was actually a giant set that was made to look like it was in regular proportions even though it wasn't.

That's one cool shape, my friend! 👍

The macro camera is incredible

Love the Macro shots :D

Great video Matt, this particular model is made using 30 x 108° modules, which were independently discovered by Robert Neale and Lewis Simon. I always find it difficult to create a perfect 3 colouring, but I find the 5 much easier. Of course you need 5 colours on a face which is easy enough, but a simple rule can be used which ensures a perfect colouring every time. Take 5 units of different colours and assemble as a sort of saw horse shape, then for the next two in the pentagonal face, look at the colour opposite. You will end up with a ring of 5 and 5 struts standing up. Using the rule as before, create a ring of 10. Then use 5 units to make the top struts and finally a ring of 5 to make the top face. Also, another way to visualise it is to imagine the edges being flat planes. All edges of the same colour will appear at 90° to each other, forming a cube shape. Interestingly too, 6 colours works nicely and can be viewed as bands of colours running around the model. Finally, if you look at the vertices of the Dodecahedron, you can inscribe 5 separate Tetrahedra, which forms the construction of a Compound of Five Tetrahedra. This is a particularly useful concept if colouring an origami model which uses 'verticies' modules. This model uses edge modules and there are of course origami models which use face modules too.

What on earth is with the random size changes? It looks like Matt is playing with us by swapping in larger/smaller items during the close-ups and wide shots, just to get one over on us :P