How many ways can you join regular pentagons?

Thanks to Jane Street for supporting this video.

Curved-Crease Sculptures by Erik Demaine and Martin Demaine

Cookie. Clicker. Like that video is going to happen.

CORRECTIONS
- None yet, let me know if you spot anything!

Filming and editing by Alex Genn-Bash
Written and performed by Matt Parker
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician

[standupmaths]

I meant what I said: 50k likes and Cookie Clicker video gets made. But I'm pretty sure I'm safe.

[goodboi]

I hope Matt has underestimated how much the community NEEDS a Cookie Clicker video.

[ChickenGeorgeClooney]

This feels like a rare instance where the cardboard objects aren't meant to represent broader mathematical concepts, but rather its literally about what you can do with cardboard pentagons.

[merseyviking]

There's a definite discontinuity where Matt goes from saying they have to be planar pentagons, to where he makes them very much non-planar. I get why now, but it felt like it was never explained why the rules can be relaxed.

[ErikScott]

For the past two years, I've taken to wrapping my Christmas gifts in custom boxes of various complex shapes made up of various polygons. The box essentially becomes part of the gift, which makes it fun, especially if the gift itself is otherwise boring or expected. This video has given me some ideas for new gift boxes. Figuring out how to wrap them in paper will be especially interesting, though.

[thomasblok]

I appreciate how Matt highlights these mathematical papers that we would never see otherwise, describes them in an easy to understand way, and then actually builds the shapes. I doubt with those papers whether any physical copies were made. Bravo Matt for taking something from abstract maths and making it concrete an tangible for all of us.

P.S. I feel like the four pentagon ones are a very elegant and simple example of the same net folding into three different shapes. Definitely simpler than any of the constructions in the video about those. They are also all easily seen to be distinct.

[chipacabra]

I admire Matt's courage in scoring a bunch of papers straight on the table without any protective surface.

[Imperial_Squid]

I love that it's called a "degenerate" polyhedra, feels like when maths people call a solution "trivial" but it's even more judgemental about it, like you can almost hear the mathematician saying "yeah, i guess, but you *_know_* that's not the answer i was looking for..." 😂😂

[pastek]

I strive to get as much joy in my life as Matt when he sees colored cardboard pieces

[mrsqueaksrules]

Matt, as someone who's clinically conditioned to click cookies continuously, you don't know how much I need a cookie clicker video.

(I tried to keep the alliteration going, but I couldn't quite conjure continuing 'c' words.)

[AstrumGV]

I suppose the question isn't how many polygons exist that have pentagons as surfances, but how many polygons can we make, of which all surfaces can be constructed out of uninterupted pentagons.

[tobybartels]

The subtle difference between a convex polyhedron made by sticking regular pentagons together, and a convex polyhedron with regular pentagonal faces.

[OrnateFail]

For the trio of names I propose: Hamburger, Hotdog, and Pasty. All ways of holding your meal! If you absolutely need to make them alliterative, may I reluctantly offer “Handwich”.
Also I’d love a video on Cookie Clicker!

[Elesario]

I mean... I always like Matt's videos, so it's a no brainer that I'd want to see a Cookie Clicker video, even though until now I'd never heard of such a game.

[brcktn]

Finally, the long awaited sequel to "Every Strictly-Convex Deltahedron"

[ThomasWinget]

I think my favorite part of this is that all of the constructions require by definition that the folds join vertices, meaning if you start from a set of regular shapes as you did then all of the folds are simply "fold along the line made by these two vertices". This means that this could become an exercise in classrooms without a lot of hassle, and that's just awesome. I'd have thoroughly enjoyed doing something like this in school.

[OverkillSD]

It's a regular pentagon where regular pentagon is defined as the pentagon that Matt just drew.

[IstasPumaNevada]

I always love a Maths & Crafts video from Mr. Parker.

[Johan]

I feel like this video was the first time I actually grokked external angles. Somehow the definition got stuck in my head without ever actually filling out as a concept. Ah the random holes in our educational journeys, thanks for patching this one!

[privacyvalued]

It's nice to see Matt's inner 5 year old come out with making colorful construction paper objects. I liked the video. Looking forward to the Cookie Clicker video!