|Fig 950.12 Three Self-Packing, Allspace-Filling Irregular
Tetrahedra: There are three self-packing
irregular tetrahedra that will fill allspace without
need of any complementary shape (not even with the
need of right- and left-hand versions of themselves).
One, the Mite (A), has been proposed by Fuller and
described by Coxeter as a tri-rectangular tetrahedron
in his book Regular Polytopes, p.71. By joining
together two Mites, two varieties of irregular tetrahedra,
both called Sytes, can be formed. The tetragonal
disphenoid (B), described by Coxeter, is also called
the isosceles tetrahedron because it is bounded by
congruent isosceles triangles. The other Syte is formed
by joining two Mites by their right-triangle faces
(C). It was discovered by Fuller that the Mite has a
population of two A quanta modules and one B
quanta module (not noted by Coxeter). It is of interest
to note that the B quanta module of the Mite may
be either right- of left-handed (see the remarks of
Arthur L. Loeb). Either of the other two self-packing
irregular tetrahedra (Sytes) have a population of four
A quanta modules and two B quanta modules, since
each Syte consists of two Mites.
Since the Mites are the limit case all space-filling
system, Mites may have some relationship to
quarks. The A quanta module can be folded out of one
planar triangle, suggesting that it may be an
energy conserver, while the B quanta module can not,
suggesting that it may be an energy dissipator.
This gives the Mite a population of two energy conservers
(A quanta module) and one energy dissipator
(B quanta module).
Copyright © 1997 Estate of R. Buckminster Fuller