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
Gear Cube another four gears out and replaces them with standard edges. As the amount of gears get fewer and fewer, the difficulty level rises. So four sides can make 90° turns whereas the fifth and sixth sides are using the gear cogs giving only one option being a 180° turn. Gear Ball: This cube has two sets of edges. The outer edges are gear shaped with six teeth, and a black barrier on it. The inner edges are smaller and not circular, and only have too teeth. In addition, the corners have a three-pronged barrier. This cube is manufactured by Mefferts,