Complex Projective 4-Space

Abstraction: Constructing first known golyhedron from golygon generalization

Key points:

• A golygon is a right-angle lattice polygon with consecutive integer side lengths; all golygons have n = 8k edges
• A golyhedron is the 3D analogue: a lattice polyhedron on integer lattice with axis-parallel edges and face areas forming a set {1, 2, ..., n}
• Joseph O'Rourke conjectured no golyhedra exist; the author disproved this by constructing one with 32 faces
• Construction uses a chain of unit cubes with L-shaped faces in pairs whose areas differ by 2, terminated by "club-foot constructions"
• The minimum number of faces for any golyhedron is bounded between 11 and 32; exact minimum remains an open problem

Connections: Mathoverflow · Combinatorics · Discrete Geometry

Source: https://cp4space.wordpress.com/page/11/