> We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we

> We find a remarkably simple structure: simple categorical concepts are represented as simplices, hierarchically related concepts are orthogonal in a sense we make precise, and (in consequence) complex concepts are represented as polytopes constructed from direct sums of simplices, reflecting the hierarchical structure. It's satisfying that the structure is precisely the one you would hope for.