Lambda cube are replaced by faces, as well as a dual representation as a dodecahedron, where the 12 edges are replaced by faces. Lambda cube In mathematical logic and type theory, the λ-cube is a framework for exploring the axes of refinement in Thierry Coquand's calculus of constructions, starting from the simply typed lambda calculus (written as λ→ in the cube diagram) as the vertex of a cube placed at the origin, and the calculus of constructions (higher-order dependently typed polymorphic lambda calculus; written as λPω in the diagram) as its diametrically opposite vertex. Each axis of the cube represents a new
Partial cube partial cube labeling. The isometric dimension of a partial cube is the minimum dimension of a hypercube onto which it may be isometrically embedded, and is equal to the number of equivalence classes of the Djoković–Winkler relation. For instance, the isometric dimension of an formula_9-vertex tree is its number of edges, formula_13. An embedding of a partial cube onto a hypercube of this dimension is unique, up to symmetries of the hypercube. Every hypercube and therefore every partial cube may be embedded isometrically into an integer lattice, and the lattice dimension of the partial cube is the minimum dimension of