Quantum may be used in the sense of "fundamental unit or increment." In synergetics, polyhedra analyze into fundamental increments of volume known as quantum modules, or mods for short. The A and B mods derive from the regular tetrahedron and octahedron respectively. The tetrahedron consists of 24 A modules, 12 left handed and 12 right handed (or, alternatively, 12 inside out and 12 outside out -- inside-outing being another way of changing handedness, a left handed glove being an inside out right handed glove).
24 A modules comprise the regular tetrahedron. As the latter is ascribed a volume of 1, each A-mod has a volume of 1/24.
The regular octahedron is comprised of 48 A mods and 48 B mods. Since A and B mods have equal volume, the total volume of the octahedron is 4 (96 times 1/24). Other polyhedra in the synergetic hierarchy, excepting those of 5-fold symmetry, may also be assembled from combinations of A and B modules.
An irregular tetrahedron comprised of 2 A's and 1 B, known as the MITE (minumum tetrahedron) is the simplest -- in terms of fewest edges etc. -- space filler. Left and right handed MITEs are outwardly identical. 8 MITEs assemble the space-filling, unit-volume Coupler (see below), an irregular octahedron formed by connecting the centers of face-bonded, space-filling rhombic dodecahedra. 24 MITEs assemble the cube.
Space-filling cubes also define Couplers. Their common square
faces define longitudinal slices through these irregular octahedra,
creating half-couplers or
Kites (volume 1/2). Individual cubes
are comprised of 6 such half-couplers, for a volume of 3. The
half-couplers defined by rhombic dodecahedra are sliced along an
axis perpendicular to the cube-face cuts. Twelve such half-couplers
make up the space-filling rhombic
dodecahedron (volume 6).
At his SpringSpace website, Karl Erickson explores A and B mods, MITEs and Couplers, by means of Gerald de Jong's StruckJava, an interactive geometry applet based on the concept of 'elastic intervals' or 'springs'.
The topic of modules links to a broad range of historical and contemporary investigations, both internally and externally to Synergetics. For example, David Koski has developed an elegant set of modules for constructing shapes having five-fold symmetry, which the A and B mods cannot encompass. Koski begins by carving up the 'golden cuboid', a brick-shaped volume of edges phi, 1 and 1/phi. The resulting tetrahedra (one of which is the same shape as the Synergetics T mod though differently scaled), comprise the basic templates, and may find their linear dimensions rescaled by powers of phi when participating in various five-fold symmetric assemblies.
Yasushi Kajikawa has innovated an alternative approach to modularizing the five-fold world, using three edge lengths to construct his ten template shapes.
These explorations link to those of Roger Penrose and many others.
For further reading:
Graphics by Richard Hawkins [rh] using Alias Animator V5.1 on an SGI Indigo2 Extreme