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
Folded cube graph as many vertices, by identifying together (or contracting) every opposite pair of vertices. An order-"k" folded cube graph is "k"-regular with 2 vertices and 2"k" edges. The chromatic number of the order-"k" folded cube graph is two when "k" is even (that is, in this case, the graph is bipartite) and four when "k" is odd. The odd girth of a folded cube of odd order is "k", so for odd "k" greater than three the folded cube graphs provide a class of triangle-free graphs with chromatic number four and arbitrarily large odd girth. As a distance-regular graph with odd