Positioning points inside a triangle

[fael097]

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_Lab/assets/images/home/SV40_particle.jpg

it has a icosahedral geometry and 72 capsomeres (the flower things) arranged on its triangles, like this picture:

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.

thank you in advance!

 

[jvicens]

Hello,

I can offer some insight into the proper arrangement of capsomeres on a triangle in an icosahedral polyomavirus. The arrangement of capsomeres on a triangle is determined by the symmetry of the virus, which is based on the icosahedral geometry.

In an icosahedron, there are 20 equilateral triangles, each with three vertices. The capsomeres are arranged at the vertices of these triangles, with one capsomere at each vertex. This means that each triangle will have three capsomeres at its vertices.

The remaining capsomeres are then arranged inside the triangle, with one capsomere at the center and the other two equidistant from the center and the vertices. This arrangement ensures that each capsomere is equally spaced from the others surrounding it.

To achieve this, the distance between the center capsomere and the vertex capsomeres will be slightly shorter than the distance between the vertex capsomeres and the other capsomeres inside the triangle. This creates a slightly curved surface, as seen in the image provided.

I hope this helps to answer your question. If you have any further inquiries, please don't hesitate to ask. Thank you for your interest in this fascinating topic!