The convex hull of the Genesis scale

This turns out to be a complicated, literally multifacted structure in the four-dimensional space of octave equivalence classes. There are 22 vertices, 21 interior points, and 38 facets, or cells. The vertices (extreme points) are

81/80, 33/32, 21/20, 16/15, 11/10, 32/27, 11/9, 14/11, 9/7, 21/16,
7/5, 10/7, 32/21, 14/9, 11/7, 18/11, 27/16, 20/11, 15/8, 40/21, 64/33, 160/81

The interior points are

1, 12/11, 10/9, 9/8, 8/7, 7/6, 6/5, 5/4, 4/3, 27/20, 11/8, 16/11,
40/27, 3/2, 8/5, 5/3, 12/7, 7/4, 16/9, 9/5, 11/6

This is a little more complicated than I had hoped for, in that it makes analyzing Genesis from this point of view something of a chore.