The distance from P to three sides is 3/2a of the root; As long as we understand what is better than what, the problem is to compare a regular triangle to a regular tetrahedron, so what is the relationship between the root number 3/2 * a and a regular triangle? Answer that 2/3 A of the root sign is the height of the regular triangle. By analogy, the answer in the past should be the height of the regular tetrahedron, so it is the square root of 6/3 a. However, this problem can be thought of as follows: in a regular triangle, the point is fixed at the position of a vertex, the distance to two sides is 0, and the distance to the other side is high, so if the sum of the distances to three times is a fixed value, it is high. Regular tetrahedron is the same, fixing a point to a vertex, the distance to three of them is zero, and the distance to the other surface is high. If the sum of the distances to the four surfaces is a constant value, it is equal to the high general situation. From 2-D analogy to 3-D, a point corresponds to a line, a line corresponds to a surface, and a face corresponds to an object. The angle between two straight lines corresponds to the angle between two planes, and so on. You need to experience it yourself.