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
Klee–Minty cube algorithms and also for interior-point algorithms. The Klee–Minty cube was originally specified with a parameterized system of linear inequalities, with the dimension as the parameter. When the dimension is two, the "cube" is a squashed square. When the dimension is three, the "cube" is a squashed cube. Illustrations of the "cube" have appeared besides algebraic descriptions. The Klee–Minty polytope is given by This has "D" variables, "D" constraints other than the "D" non-negativity constraints, and 2 vertices, just as a "D"-dimensional hypercube does. If the objective function to be maximized is and if the initial vertex for the simplex algorithm