Where does cube collide?

In geometry a cube is the regular hexahedron: a convex polyhedron bounded by six congruent square faces meeting three at each of its eight vertices, one of the five Platonic solids and the three-dimensional member of the family of measure polytopes. Coxeter's Regular polytopes (1973) places it within the systematic theory of regular figures across dimensions. The referent is a geometric solid defined by its symmetry and face structure, and it is unrelated to a database aggregation or a backgammon stakes device despite the shared word.[1]

Unit

A regular solid with six square faces, eight vertices, twelve edges

Recovery means

Not applicable

Measured by

Characterized by edge length, symmetry group, and its face, edge, and vertex counts

In databases and online analytical processing a cube is a multidimensional structure that precomputes aggregates of a measure across every combination of dimensions, so that totals and subtotals can be sliced, diced, and rolled up along any axis. Gray and colleagues' 1997 Data cube: A relational aggregation operator generalizing group-by, cross-tab, and sub-totals defined the operator that generalises grouping to all dimensional combinations at once. The referent is an aggregation operator and the materialised result it produces for analytic queries, and it has nothing to do with a geometric solid or a backgammon stakes die beyond the word.[2]

Unit

Precomputed aggregates of a measure across all dimension combinations

Recovery means

Not applicable

Measured by

Realized as the materialized aggregates queried by slice, dice, roll-up, and drill-down