Sunday, May 19, 2013

Decahedron.





It's a 10 sided polygon.

Does anyone know what "Bucky Balls" are?
They're small magnetic balls that are very expensive lol. Not that expensive, just more than you'd like.
Anyways, a guy on youtube made a decahedron and displayed it.
My friends and I joked how many balls it took to make that. Then I realized I really wanted to figure it out.
Boring and mathematical? Fuck yeah..
But after everyone's gone to sleep and you can't debate philosophy with anyone then what else is there?

A rough explanation:
  • Each side is 12 'balls' long 
  • There are 10 total faces to this shape
  • You need the area to figure out the volume.
I don't know if I'm even correct but after a few hours of looking up formulas and making pretty diagrams I came to the total of: 1200 balls. 

Isn't that weird? 10 faces and each side is 12 balls long. Coincidental. 
I'm sure there is another 10 somewhere in there which would make 10*10*12=1200.
That would be a very each calculation.
I didn't go that route. 



The youtube video:

http://www.youtube.com/watch?v=InNtkQiucTo


Decahedron - 10 Sided polyhedron
    Area of a Triangle = ½(base*height)
    Volume of a Pyramid = Area of a Triangle * Height * 1/3
    Volume of a Decahedron = Volume of a Pyramid * 10

a² + b² = c² OR a² + x² = c²
6² + x² = 12²
36 + x² = 144
x² = 108
x = 10.39230484541326
x = 10 (“Bucky Balls” are integers)

Area of Triangle = ½(base*height)
Area of Triangle    = ½(6*10)
                             = ½(60)
                             = 30

Multiply area of Triangle by 2 because 30 is only half the area of one surface.
Area of triangle = 60

Volume of a Pyramid = Area of a Triangle * Height * 1/3
Area of Triangle = 60
Height = 6 (following the
Right triangle rule).
Volume  = 60 * 6 * 1/3
              = 360/3
              = 120
So, out of every 10 parts of a decahedron each contains 120 “bucky balls”.

Volume of a Decahedron = Volume of a Pyramid * 10
Multiply by 10 because there are 5 surfaces on each of the 2 sides.

This decahedron contains 1200 “Bucky Balls”.

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