Regular Tetrahedron

You will select X points within the volume occupied by a regular tetrahedron with edge length of 2 units. The condition is that there should be at least 1 unit distance between each of these points. What is the maximum possible value of X?

Note: The surfaces of the regular tetrahedron (including the edges and the vertices) are considered within the volume.

answers: # 106     popularity: 75.0 %     difficulty: 18.8 %