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
Rubik's Cube group define orientation. One choice is the following group, given by generators (the last generator is a 3 cycle on the edges): Since "C" is a normal subgroup and the intersection of "C" and "C" is the identity and their product is the whole cube group, it follows that the cube group "G" is the semi-direct product of these two groups. That is Next we can take a closer look at these two groups. The structure of "C" is since the group of rotations of each corner (resp. edge) cube is formula_30 (resp. formula_31), and in each case all but one