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
Prince Rupert's cube by the two opposite points, as in the case of Prince Rupert's problem. If the aspect ratio is not constrained, the rectangle with the largest area that fits within a cube is the one that has two opposite edges of the cube as two of its sides, and two face diagonals as the other two sides. Alternatively, one may ask for the largest formula_4-dimensional hypercube that may be drawn within an formula_5-dimensional unit hypercube. The answer is always an algebraic number. For instance, the problem for formula_6 asks for the largest cube within a four-dimensional hypercube. After Martin Gardner posed