The A and B Quanta Modules are the two irregular tetrahedra, each 1/24 the volume of a regular tetrahedron, from which Fuller assembles every symmetric form in synergetics and by which its volumes resolve into whole numbers.

A and B Quanta Modules

Two dissimilar irregular tetrahedra of identical volume — each 1/24 of a regular tetrahedron — that are the minimum volumetric "quanta" from which all the symmetric forms of synergetics are built.

The A and B Quanta Modules are Fuller's tetrahedral "atoms": the smallest, simplest volumetric units into which the closest-packed geometry of synergetics resolves. Each is an irregular (asymmetrical) tetrahedron with a volume of exactly 1/24 of the regular unit tetrahedron, so that 24 modules compose one tetrahedron. The A Module is 1/6 of a Quarter-Tetrahedron: slicing a quarter-tetrahedron by three internal perpendicular planes yields six identical asymmetric pieces — three positive (right-handed) and three negative (left-handed) — each 1/24 of the tetra (§913.01). The B Module is derived instead from the octahedron: it is 1/6 of the fractional unit left when a Quarter-Tetrahedron is subtracted from an Eighth-Octahedron, again giving six pieces of 1/24-tetra volume, three positive and three negative (§916.01). Both modules unfold from a single planar triangular net and fold back up into a whole irregular tetrahedron — the A into one scalene triangle, the B into four interhinged 90-degree triangles (§914.01, §921.12–.13).

Although the A and B Modules have the same volume, they are not mirror images and behave differently as energy containers. Fuller frames the A Module as circumferentially embracing, energy-impounding, and nucleation-conserving ("outside-inwardly introvertive"), while the B Module is disintegrative and exportive ("outside-outwardly extrovertive"), releasing energy roughly four times faster (§921.20–.40). He draws a deliberate analogy to the intertransformable proton and neutron and their difference in mass, noting the modules' equal volume but "uniquely different energy-transforming capabilities" (§921.03). A Modules can combine with one another in three ways to make a whole regular tetrahedron and with B Modules in seven further ways, each yielding a single whole tetrahedron (§921.20–.21).

The modules combine in whole-number counts to build every symmetric form. The pivotal assembly is the Mite — a contraction of Minimum Tetrahedron — made of two A Modules and one B Module (AAB), a three-module irregular tetrahedron that is the simplest all-space filler in Universe (§953.10, §986.421). Within a Mite one A is positive and one negative, and the B carries the Mite's sign; Mites themselves come in positive and negative forms and can pack to fill all space (§953.20). Larger polyhedra follow as clean module tallies: the tetrahedron is 24 modules, the cube 72, the octahedron 96, the rhombic dodecahedron 144, and the vector equilibrium 480 (§982.02–.04, §954.10, §955.04).

Because every synergetic form is an integer number of these 1/24-tetra units, the volume hierarchy comes out in rational whole numbers with the tetrahedron as unity: tetrahedron = 1, cube = 3, octahedron = 4, rhombic dodecahedron = 6, vector equilibrium = 20 (§982.02–.04). This is why the modules matter — they are the volumetric quantum that makes synergetic geometry a low-integer accounting system rather than a catalogue of irrational decimals. Fuller treats the Mite (and its assemblies, the Sytes and Couplers) as the "prime quanta" of all-space filling, and even ventures a kinship between the AAB module set and the quarks (§954.44, §986.453–.454).

Sources

Synergetics — Fuller's primary text: §910–§923 (A and B Quanta Modules; A Module §913, B Module §916, Functions §920, Energy Deployment §921), §953 (the Mite / Minimum Tetrahedron), and §982.02–.04 (module counts and whole-number volumes)
Fuller's Coined & Redefined Terms

quanta-modulesa-moduleb-modulemitesynergeticstetrahedrongeometrybuckminster-fuller

A and B Quanta Modules

A and B Quanta Modules

See Also

Sources