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math.CO2026
The smallest square tileable by pairwise incomparable integer rectangles
George M. Georgiou
Croft, Falconer and Guy ({Unsolved Problems in Geometry}, Problem~C5) exhibit a tiling of the square by eight pairwise incomparable integer rectangles and remark that…
math.CO2026
Congruent Triangular Faces, Reflections Allowed: Universal Realization and the Minimum Face Count in Problem B22
George M. Georgiou
Problem B22 in Unsolved Problems in Geometry asks which triangles occur as the common face of a convex polyhedron, how many copies are needed, and how they may be arranged. We sett…