2 problems

A special octagon is a lattice octagon whose opposite sides are parallel with slopes $0$, $\pm1$, and $\infty$, and which has an axis of symmetry parallel to a pair of sides. Speci…

A Hexhouse is the lattice polygon obtained by placing a trapezoid on top of a square, with its moduli described by three integral parameters. Hexhouse periodicity conjecture. Every…