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.
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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