Mathematical Impressions: Goldberg Polyhedra

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10 жыл бұрын

Because of their aesthetic appeal, organic feel and easily understood structure, Goldberg polyhedra have a surprising number of applications ranging from golf-ball dimple patterns to nuclear-particle detector arrays.
www.simonsfoundation.org/multi...

Пікірлер: 44

@reelrook3044 7 ай бұрын

Mind Blown! I've been working with polyhedra since 2009 and I still learn new things every day. This was Amazing!

@IAmQb 8 жыл бұрын

Nice video! Also, it's a 3,1-Goldberg polyhedron

@Boomshankarim 8 жыл бұрын

My mind is blow away right now. All my life I've been looking for ways to regularly divide the surface of a sphere into regular polygons and I always thought the soccer ball to be maximum you can reach. The Goldberg method finds a simple solution to this complex problem. Fascinating stuff. Thanks

@lyrimetacurl0 4 жыл бұрын

They aren't regular though, the soccer one is the regular polygons one.

@pocarski 8 ай бұрын

I feel a bit silly replying to a 7 year old comment, but: - The soccer ball is the only Goldberg polyhedron made with regular polygons. In all others, three hexagons meet at a vertex, which would make a flat surface if they were regular. - There are ways to split a sphere into more polygons than the soccer ball. The record of 92 regular polygons belongs to something called the "snub dodecahedron" which is made up of 12 pentagons and 80 triangles. It doesn't have mirror symmetry, so there are two variants of it.

@iqbaltrojan 4 жыл бұрын

Please make more Mathematical Impressions!

@theskv21 8 жыл бұрын

Your videos are a delight. Thank you so much!

@TheRojo387 4 жыл бұрын

The 1-0 Goldberg polyhedron is the regular dodecahedron; there, I had to say it!

@YASxYT 8 жыл бұрын

this video needs more views

@Weltaz 5 жыл бұрын

Wohw !!! Fantastic ! Merci beaucoup 😄

@NonTwinBrothers 2 жыл бұрын

Classic George Hart, I remember seeing these back in middle school. Best thing ever

@genna87 6 жыл бұрын

How did you realize the wooden models? There's any tutorial to make it starting from the paper model?

@abdulrhmanaun 2 ай бұрын

That's unbelievable 🤩

@YoAddicts 8 жыл бұрын

Very very very cool

@warlockpaladin2261 2 жыл бұрын

Okay... that was impressive.

@ponderbot34 5 жыл бұрын

I need to know... Do all of the faces touch the insphere? Do all vertices touch the circumsphere? Do all edges touch the midsphere? I know the goldberg polyhedron of (m,n) is the dual of a geodesic polyhedron of (m,n).

@CharTheDude 8 жыл бұрын

What's the model of 3D printer you use to get such detailed models?

@pratherat 8 жыл бұрын

Maybe shapeways?

@sebastianjost 3 жыл бұрын

Any resin printer can probably achieve this.

@Kurtlane 8 жыл бұрын

Aren't Buckminster Fuller's geodesic domes also Goldberg polyhedra?

@niveditamaster1362 4 жыл бұрын

Yes, but they are divided into triangles, so they are called ‘geodesic’

@lockeisback 8 жыл бұрын

how can there be sections of the surface with 7 hexagons all touching? wouldnt that make it flat? the only way i can think of is if some are smaller than others or if they aren't regular hexagons

@fabricioguido8202 8 жыл бұрын

+Locke Demonthenese I was thinking the same thing: If 3 hexagons touch each other, then they would be flat, so they wouldn't be independent faces!

@romanr9883 8 жыл бұрын

well because they arent flat. they are actually curved. like the football example

@boscorner 7 жыл бұрын

Locke Demonthenese i think it's because although the pentagons are always regular, the hexagons may not be.

@wpbn5613 6 жыл бұрын

They aren't regular hexagons. You're right

@VyxtheBat 4 жыл бұрын

They aren't flat. As he said in the video, the final spherical shape is actually "blown up" upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Goldberg_10_0_equilateral-spherical.png/540px-Goldberg_10_0_equilateral-spherical.png

@GieneqAD 9 жыл бұрын

Cool :D

@rainverrev2307 7 жыл бұрын

Can you make fair dice in the shape of a Goldberg Polyhedra?

@KnakuanaRka 7 жыл бұрын

Rain Verrev No, all the faces have to be identical.

@xxnotmuchxx 8 жыл бұрын

How many different Goldberg polyhedra are there?

@boscorner 7 жыл бұрын

Topsoil Depletion Awareness"there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle." www.ncbi.nlm.nih.gov/pmc/articles/PMC3939887/#!po=14.2045 page 7

@boscorner 7 жыл бұрын

Topsoil Depletion Awareness so to answer your question, an infinite amount of them. according to this article