positioning points inside a triangle
 

hello people, i'm a 3d modeler and animator, and i have a question regarding triangles.

this is a polyomavirus,
http://www.brown.edu/Research/Atwood...0_particle.jpg
it has a icosahedral geometry and 72 capsomeres (the flower things) arranged on its triangles, like this picture:
http://www.umass.edu/molvis/workshop/sv40_1w.gif
if i pick a triangle, i can see that it has one capsomere in each vertex and three arranged inside the polygon. my question is how to properly arrange these 3 capsomeres in each triangle. if you take a closer look at the picture, you'll notice that each vertex' capsomere has 5 others capsomeres around it, and the other capsomeres (those arranged inside the triangles) have 6 others. they have to be distanced equally from all the capsomeres surrounding them.

capsomeres are positioned closer to one end of the edge than the other, but it's a question of rotation, not mirroring. the structure is a perfect icosahedron, and the three dimensional structure doesnt matter, it's all about the triangle

thank you in advance!