I’m very familiar with Fuller’s A, B, S, T&E modules. 2 As (left and right) + 1 B (left or right) make a Mite, a space-filling tetrahedron of no handedness (left = right) also inventoried by D.M.Y. Sommerville in the 1920s. Aristotle was right: tetrahedron’s do pack to fill space, just not regular ones.
As you say, A & B (also T) have volume 1/24 (of the regular tetrahedron), and we would typically use those to build: tetrahedron of volume 1, cube of volume 3, octahedron of volume 4 (so not two cubes), rhombic dodecahedron of volume 6 (two cubes). The Mite has a volume of 1/8 and 24 of them make a cube.
My colleague David Koski has done a huge amount of work with the T, E and S modules. If you scale these by phi, up and down, then you may use them to express the volumes of five-fold symmetric shapes, such as the icosahedron and pentagonal dodecahedron.