COUPLERS pack into Rhombic Dodeca in allspace. One COUPLER can integrate either as whole or half into six possible different Rhombic Dodecahedral domains. There are only four different rhombic dodeca lattices in allspace because rhombic dodeca on opposite sides of the two rhombic equators in the COUPLER are part of the same lattice. The COUPLER LATTICE integrates all four RD lattices and outlines some of the redundancies (interpenetrating RD) found in allspace mitepacking. See SIAMESE COUPLERS for other redundancies involving the RITE. The four rhombic dodecahedral lattices in allspace correlate with the four IVMs (isotropic vector matrices) discovered by Russell Chu and explained in his essay: "Mapping the Hidden Patterns of Sphere Packing". In the model above,the two yellow RD correlate with the Tetrahedral A IVM; the two green RD, Tetrahedral B IVM; the red RD, Octahedral C IVM; and blue RD , Cuboctahedral D IVM. In relation to the 4 IVM, the CUBOCTAHEDRAL D RD lattice is non-nucleated and centered on the RD; the TETRAHEDRAL A & B RD lattices are nucleated at the 3-valent vertices of the RD; and OCTAHEDRAL C lattice is nucleated at the 4-valent vertices of the RD.
PATTERN RECOGNITION IN ALLSPACE MITEPACKING