Half a croissant, on a plate, with a sign in front of it saying '50c'
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Hula hoop polyhedron

Construction toy to build a big ball
  [vote for,

This is just a kit of hula hoops and clamps to make a big ball.

The ball can be rolled around, jumped into, etc. Fun at the beach or at the playing field. Covered in towels makes a cubby house or sun shelter. Someone will inevitably try and climb up the ball which will eventually cause it to collapse. Fun.

To use an icosahedron as an example, the kit comprises 20 hula hoops and 30 clamps.

The clamps have a hinge on one side and a locking mechanism in the other side. When in the closed state the clamp forms two adjacent cylindrical (or more correctly toroidal segment) holes to fit a small portion (e.g. 5cm) of two hula hoops. The inner surface of the clamps would be made of an elastic material to conform to the hula hoop. The outside of the clamp would also be covered in a soft material so it doesn't hurt kids as they play.

To assemble, take a hula hoop and clamp three hula hoops equally spaced around it. Fold hoops together at the dihedral angle and clamp touching hula hoops. Repeat until icosahedron is formed.

More advanced kits could have hula hoops of two (or more) different sizes to made more complex polyhedra (e.g. truncated dodecahedron).

xaviergisz, Nov 12 2021

H type tube connector https://images.app....l/fAiG9ULGWfrmSb4t5
[xaviergisz, Nov 12 2021]

Mini prototype https://www.amazon..../dp/B00ZRD99C0?th=1
What you're doing only smaller & one-piece-molded [neutrinos_shadow, Nov 15 2021]

I made it! https://imgur.com/gallery/PgUpdUW
Truncated i-squash-ahedron [xaviergisz, Dec 06 2021]


       I like the idea of a 'geometric solids' construction kit but using simple hula hoops and clamps is a really nice idea. As you mentioned, you will need different sized hula hoops to take the place of the pentagons and hexagons in the truncated icosahedron, or the triangles and pentagons in the icosadodecahedron
hippo, Nov 12 2021

       "Having a ball?"   

       "Well, not exactly ..."   

pertinax, Nov 12 2021

       “Billy! How many times do we have to tell you not to lock your little brother inside the hulahehron?!”   

       + That is nice. Please be sure to include picture directions for me! I want mine in blue.
xandram, Nov 12 2021

       Thought this might be a hulahoop with a circular inside ring but featuring a polygon disc on the outside edge. This would enable it be used as both a Hula Hoop and as a component to create a geodesic dome. (see Buckminster Fuller)
xenzag, Nov 12 2021

       That first link doesn't hardly bakes this at all: 1) They only made tetrahedra and a not quite Sierpinski tetrahedron, not icosahedron or other large balls as described here. 2) It looks like they just used twisted pipe cleaners rather than specially designed clamps to hold these together, leading to the structural collapse shown in the last photo.
scad mientist, Nov 12 2021

       One note about the design: If you create //(or more correctly toroidal segment)// the angle between the adjacent hula hoops will be fixed, so if a set of clamps is good for an icosahedron they won't be quite right for a dodecahedron. This shouldn't be too hard to resolve.
scad mientist, Nov 12 2021

       I'm going to buy 60 H-type tube connectors (two for each edge for added strength/stability) and 20 hula hoops to test out the idea.
xaviergisz, Nov 12 2021

       [xaviergisz], nice! Please link photos of all 5 once you're done experimenting.
& as [scadmientist] wrote, you want the connectors short (as per the "H type") or hinged; not a fixed pair of large curves as in the idea. A hinge doesn't need to be "locked"; the system (once complete) will be stable even with "free" hinges (although the hula hoops, being flexible, will allow some movement, but then that's probably a good thing...).
neutrinos_shadow, Nov 14 2021

       I've decided that an icosahedron is not going to be strong enough, so I'll be making a truncated icosahedron. This will require 32 hula hoops: 20 large and 12 smaller. I've found hula hoops of 91cm and 71cm diameters, which I think is just about right.
xaviergisz, Nov 14 2021

       //not going to be strong enough//
Given that the hula hoops are (presumably) a little flexible, more hoops means less strength/rigidity. A dodecahedron would be your best bet (each hoop connected to 5 others). Also, a truncated icosahedron (with the hoops you mention) will be rather large...
neutrinos_shadow, Nov 14 2021

       I would suggest cutting semi circles from the inside curves of outer hoops where they intersect inner hoops, like a spherical log house design.
This would let you attach them with a single bolt/lock washer/nut at each connection and the curvature of each cut will, while weakening the individual hoops themselves, lock the whole sphere into a much more rigid shape than if each hoop retained its full rigidity.

       //Given that the hula hoops are (presumably) a little flexible, more hoops means less strength/rigidity.//   

       Once I have the connectors and hoops I'll be able to experiment to find the strongest structure.   

       //Also, a truncated icosahedron (with the hoops you mention) will be rather large...//   

       Yep, about 2.4 meters high.   

       If all goes well I'll try for even bigger structures. For example a rhombic triacontahedron.
xaviergisz, Nov 15 2021

       Suggestion: find the right diameter/flexibility plastic pipe/rod & make your own hoops. Then you can get exactly the sizes you want.
neutrinos_shadow, Nov 15 2021

       I might consider modifying hula hoops (by cutting out a small segment and reattaching the ends) to get the size I want.
xaviergisz, Nov 15 2021

       [xaviergisz] nicely done! It's a little deformed looking, but baked therefore awesome.
neutrinos_shadow, Dec 06 2021

       I wonder whether the squash factor would be less if you kept things strictly platonic.
pertinax, Dec 07 2021

       Are some hoops on the market made from more flexible rod or strip than others? I have a vague memory of having a "favourite" hoop which was more rigid than some of the others which were a bit bendy
pocmloc, Dec 07 2021


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