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Author Topic: questions: measure the diameter of an icosahedron?... and contact juggling...  (Read 1358 times)

Daveid

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i mean is the diameter of an icosahedron measured from point to point, from side to side, or an average of the two? or is it not considered a diameter? or maybe is it the measure of the height of the pentagon... or is that equal to the other two averaged.

if i just measured the length of a side it wouldn't really communicate the size of it unless you're really familiar with those objects...

anyways i've got this oversized twenty sided die, and i think it'd be a good size to contact juggle and i don't know how to describe it as an object in regards to it's size.
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like I always say:dead monkeys don't fly on sticks.

Daveid

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or rather, i should say, i think it'd be cool if someone was contact juggling icosahedrons or similar objects... i don't contact juggle so i shouldn't say it'd be a good object for it, i just think it'd be cool if it was... or something.
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ta0

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I am not sure if you could get the fluid motion that is so attractive in contact juggling using an icosahedron.  But who knows, there may be something interesting that can be done.


Quote
if i just measured the length of a side it wouldn't really communicate the size of it unless you're really familiar with those objects...

I just checked Wikipedia (http://en.wikipedia.org/wiki/Icosahedron), and it so happens that the smallest sphere that contains it inside (i.e. circumscribed) has a radius close to the edge length (about 95%). So you could use the edge length to compare the size of an icosahedron to that of balls. Because opposite to a vertex there is another vertex, the diameter of the sphere is the distance "between points".

The radius of a sphere that touches the middle points of the edges is about 80% of the edge length.
And the largest sphere that can fit inside (i.e., inscribed) is about 75%.
Interestingly, the exact expressions include the golden ratio.
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