There is a common two-dimensional graphical representation of three values that are required to sum to a constant. The three values are represented by a point inside an equilateral triangle. More specifically, the values are represented by distances from the point to the sides of the triangle along lines perpendicular to each edge of the triangle (I think).

(a) What is this form of representation called? (It's impossible to search for it on the web; words like those in the title of this question bring up too much that's irrelevant.)

(b) Why is it the case that the three perpendicular distances to the edge always sum to the same constant for a given equilateral triangle?

(c) Are there extensions of this representation for three variables that are not constrained to sum to a constant? (I'm not asking about the more common way of representing three dimensions by a projection onto a page or screen that mimics the way that three dimensions appear from the perspective of an observer.)