How Did a 4v Icosahedron Transform My Breakfast Nook?

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Discussion Overview

The discussion revolves around the construction and display of a 4v icosahedron, exploring its design, materials used, and the personal experiences of participants related to similar projects. The conversation touches on aspects of combinatorial mathematics, effective resistance in resistor networks, and the aesthetic placement of such structures in home environments.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant shares their experience of creating a 4v icosahedron and provides a link to their progress and final product.
  • Another participant comments on the difficulty of changing the bulb in the structure and notes the absence of a fixture.
  • Several participants discuss their own projects involving polyhedra made from resistor networks, with one mentioning the use of combinatorial methods to derive effective resistances.
  • A participant references a Wikipedia article about the resistance properties of an icosahedron, suggesting that it halves resistance.
  • There is a light-hearted exchange about the appropriateness of displaying the icosahedron in different rooms of the house, with one participant describing their home setup and the context of the construction.
  • A participant expresses interest in creating their own sphere after school ends, indicating a desire to engage in similar projects.

Areas of Agreement / Disagreement

Participants express various viewpoints regarding the construction and display of the icosahedron, with some sharing personal anecdotes and others discussing technical aspects. There is no consensus on the best practices for display or construction methods, and multiple competing views on the technical challenges remain present.

Contextual Notes

Participants reference specific materials and methods used in their projects, but there are no detailed explanations of the mathematical principles involved. The discussion includes assumptions about the audience's familiarity with technical terms and concepts related to polyhedra and electrical resistance.

Who May Find This Useful

Individuals interested in geometry, combinatorial mathematics, DIY projects, and home decor involving geometric structures may find this discussion relevant.

rcgldr
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First starting making these back in 1973, but those are long gone. Decided to make a 4v icosahedron recently and this is what I ended up with. Web page shows the progress, and the final sphere:

4f.htm
 
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Already fixed. Wow, you were quick.
 
Looks neat... I did something smaller like that, but with resistor networks - 1/4 watt resistors soldered together into polyhedra. Actually deriving what the resistances should be was a fun exercise in combinatorics (well, for a freshman...).
 
It looks great, Jeff, but how do you change the bulb? :confused:
Hey, wait a second! You forgot to put the fixture in!
 
Rach3 said:
Looks neat... I did something smaller like that, but with resistor networks - 1/4 watt resistors soldered together into polyhedra. Actually deriving what the resistances should be was a fun exercise in combinatorics (well, for a freshman...).

You calculated the effective resistance across two vertices? That sounds like some tedious work with star/delta transforms.

Looks great Jeff.
 
siddharth said:
You calculated the effective resistance across two vertices? That sounds like some tedious work with star/delta transforms.

Looks great Jeff.

Never needed those, I just simplified things with symmetry arguments.
 
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Wow, you either drink a lot of coffee, or some cafe is wondering where all their stirrers went! :biggrin: How long were you allowed to leave it hanging from the ceiling on display in the living room before told to move it someplace better, like the basement or garage? :smile:
 
  • #10
display in the living room
It wouldn't be allowed in the living room. It's in the computer room. Kids are grown up and moved out, so my status is married with pet.

Pics of the computer room:

cr.htm
 
  • #11
I like it. Very nice design and idea Jeff. School will be over soon, and I think I'll try to create a sphere by myself.
 
  • #12
Jeff Reid said:
It wouldn't be allowed in the living room. It's in the computer room. Kids are grown up and moved out, so my status is married with pet.
Oh, okay. From the pics, I saw the couch and the stuffed toy sitting in the corner, which seemed to suggest there was a feminine hand involved in the decorating of the room, and figured it was a living room. I didn't think the same person who carefully placed a little stuffed toy and frilly thing in the corner of the couch would be too thrilled with a geodesic dome made of coffee stirrers decorating the living room. :biggrin: I guess the living room is just where the construction took place.
 
  • #13
From the pics, I saw the couch and the stuffed toy sitting in the corner
Oh, where the "construction" took place; we call it the breakfast nook, a small room on the far side of the kitchen. It's a low usage room, so taking it over for a few days was OK. As noted, there are no stuffed animals or toys in the computer room, unless our dog brings one of her toys downstairs.

In case anyone is wondering about the v-tails in the first computer room picture, those are the fuselages of my larger radio control gliders.

Video of the white with red trim glider, 122" wingspan. The power source for launching is 60 feet of 7/16" diameter latex tubing, 210 feet of monofilament fishing line (27lb pull, 4 .25 lb model, about 50mph during launch). For storage, it's wound up on the right most orange spool you see in the 3rd computer room picture.

jrartms.wmv

Video of the white glider from the 3rd photo, 71" winspan, at a canyon ridge where there is an updraft:

jr126.wmv
 
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