Since the COUPLER is the universal mite aggregate in allspace mitepacking, it seems appropriate to focus on the coupler to discover features which differentiate the complex variables in a mitepacking. There are three different ways mites pack into COUPLERS: (1) OCTANT, whereby each mite occupies one octant domain of the coupler;(2) CROSSOCTANT, whereby at least two adjacent mites are positioned across 2 octant domains ( opposite the square equatorial plane) of the COUPLER; and (3) HYBRID, a combination of OCTANT and CROSSOCTANT packing in the same COUPLER.

With the octant packed coupler, it is necessary to view both the obverse and reverse sides outlined by the square equator in order to differentiate one coupler from another; however, with the CROSSOCTANT packed coupler, it is only necessary to view one side, either obverse or reverse, to determine the composition of mites in the coupler . This is because all 8 mites are visible from either side of the CROSSOCTANT packed coupler.

Since the triangular surface of any coupler octant is similar to half the rhombic plane defined by either of a couplers' rhombic equators and halved at the short diagonal, any coupler octant surface can also be viewed as half of the rhombic equitorial plane of another coupler in the same allspace mitepacking. This ambiguity of the domain of a coupler in an allspace mitepacking is further complicated by the fact that any coupler can be a component in each of six different rhombic dodecahedral domains in an allspace mitepacking. Because the rhombic dodeca domain centerpoint is the equivalent to a sphere (or VE) center in the isotropic vector matrix, the domain ambiguities can be resolved by defining which one (of the four possible) IVM the mitepacking is congruent with; i.e., by defining the rhombic dodecahedral lattice of the packing.

Once the rhombic dodecahedral lattice is defined, the focus is on the A or A& B module components which are visible on each of the 12 rhombic facets on each RD in the packing. The rhombic facets are composed of either: (1) 2 octant surfaces from 2 different couplers (cubic packing), or (2) one of the rhombic equitorial planes of a single coupler (kite packing).

The most recognizable feature of any RD rhombic face is the presence or absence of B module facets. Out of the four surfaces of the tetrahedral B module only 2 (face "BCE" or face "ABE") can be visible on the RD rhombic face in a mitepacking. The "BCE" Bmod facet will be aligned along either side of the long diagonal of the rhombic face and the "ABE" Bmod facet will be aligned along either side of the short diagonal. In terms of pattern recognition, there can be from 0 to 4 "BCE" Bmod facets on a rhombic face or from 0 to 2 "ABE" Bmod facets. This means that 4 MITES are visible (and interfaceable with adjacent RD) on the RD rhombic face with "BCE" Bmod facets whereas only 2 MITES are visible on the RD rhombic face with "ABE" Bmod facets. There are 48 MITES packed into one RD in allspace, so RD with all "ABE" Bmod facets have 24 MITES on the surface and 24 concealed within; RD with all "BCE" Bmod facets have all 48 MITES interfacable at the surface. Tell Andersson refers to the former as nucleated and the latter as open rhombic dodecahedra.

As mentioned above, The CROSSOCTANT packed coupler can be most easily classified in terms of mite composition (positive or negative) because only one side needs to be viewed; moreover, the CROSSOCTANT packed coupler is also unique because all eight mites display the "BCE" Bmod facet on either the obverse or reverse surface. Because of "coupler domain ambiguity", I think that all couplers (except HYBRID) can be classified by categorizing the CROSSOCTANT packed couplers only, and the "BCE" Bmod facets are the obvious feature for pattern recognition and categorization.

- Richard Hawkins 12/22/02