Number of possibilities, triangles with different colors?
Hi everybody,
I'm doing research with triangles. Here's my problem:
Imagine three points (a triangle). There are four possible colors to color an edge with. You can use the colors as often as you'd like. How many different triangles can you form? The answer isn't as straightforward as 4^3, because a rotation is not a "new triangle". My answer by just writing all 4^3=64 possibilities down and the categorize them gave 16 different possibilities. Would any of you know how to theoretically get this number instead of just writing them all down? The attachement shows all 16 triangles (in my case i swapped the four colors for four different arrows, but that doesn't matter)
Secondly, would anyone know a formula to count these possibilities? That if you would add a point that you'll be able to calculate the amount of possibilities (If you'd add a point you'll get a pyramid). My guess at first was 4^(n-1) with n being the amount of points. But if you would get a lot of points I don't think it doesn't take into account that the 3d models become symmetric, so it would count too much possibilities.
Thanks!
RattenG
Motifs_10.pdf
