Machine Learning, etc: Visualizing 7 dimensional simplex

Suppose we'd like to visualize a set of joint probabilities realizable by distributions of 3 binary variables. It is a 7 dimensional regular simplex, and we could draw a lower dimensional section of it. As an example, suppose we want to find a good 2 dimensional section of a 3 dimensional regular simplex. It seems reasonable to restrict attention to sections that go through simplex center and two other points, each of which is a vertex or a center of some edge or face. There are just 2 such sections determined up to rotation/reflection For 7 dimensional simplex, we could similarly take 3 dimensional sections determined by simplex center and 3 points, each a centroid of some set of vertices.