Rhombic Cell Analysis - A New Way of Probing the Large-Scale Structure of the Universe. I. General Considerations

A new way of probing the large-scale structure of the universe is proposed. Space is partitioned into cells the shape of rhombic dodecahedron. The cells are labelled filled'' or empty’’ according as they contain galaxies or not. The cell size is so chosen as to have nearly equal numbers of filled and empty cells for the given galaxy sample. Two observables on each cell are definable: the number of its {\em like} neighbors, $n_1$, and a two-suffixed topological type $\tau$, the suffixes being the numbers of its like and unlike {\em neighbor-groups}. The frequency distributions of $n_1$ and $\tau$ in the observed set of filled (empty) cells are then considered as indicators of the morphology of the set. The method is applied to the CfA catalogue of galaxies as an illustration. Despite its limited size the data offers evidence 1) that the empty cells are more strongly clustered than the filled cells, and 2) that the filled cells, but not the empty cells, have a tendency of occurring in sheets. Further directions of development both in theory and application are indicated.