In Synergetics (1997),R. Buckminster Fuller introduces two tetrahedral shapes:
A Quanta Module (913.00) & B Quanta Module (916.00)
The A Quanta Module can be constructed in many different ways, but the most obvious may be to divide the first of the five platonic solids , the equilateral tetrahedron, in quarters. The result are four identical irregular pyramids meeting in the centre of the original tetrahedron. A further subdivision of this quarter into six irregular tetrahedra can be achieved by division at the three perpendicular bisectors. The resulting shape is a therefore a 1/24th (a 1/6th of a 1/4th) of the original volume and assigned as being the A Quanta Module.
As the six parts are equal in all properties, they are mirror symmetrical in pairs of three. Buckminster Fuller calls them positive and negative (913.10). The A Quanta Module has a set of unique properties according to fold-ability and therefore further interesting relations to two-dimensional space, not to be further discussed here.
The second shape described in the following is the B Quanta Module. Similar to the earlier procedure, we now divide a regular octahedron in the same manner first into eight equal parts and afterwards into six pyramids. By subtracting the A Module from this shape we create the so called B Quanta Module equal in in volume and therefore also a 24th of original tetrahedron.
While Buckminster Fuller briefly mentions their functionality for closest packed space he also outlines their behaviour of asymmetrical polyhedral units.n His further investigations on the modules mainly concentrate on their meaning as the representative for energy deployment (921.00).
In polyhedral geometries these modules can be applied to many known forms.
In Synergetics, Buckminster Fuller also explores their meaning for space-filling and further refers to Coexters "Regular Polytopes".