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
Compound of 5-cube and 5-orthoplex cells and edges. Mid-edges of the 5-cube cross mid-cell in the 16-cell, and vice versa. It can be seen as the 5-dimensional analogue of a compound of cube and octahedron. The 42 Cartesian coordinates of the vertices of the compound are. The convex hull of the vertices makes the dual of rectified 5-orthoplex. The intersection of the 5-cube and 5-orthoplex compound is the uniform birectified 5-cube: = ∩ . The compound can be seen in projection as the union of the two polytope graphs. The convex hulll as the dual of the rectified 5-orthoplex will have the same vertices, but