{"id":"hexagon/2610.00015","pdf":"https://hexagonmath.org/pdf/2610.00015v1","url":"https://hexagonmath.org/abs/2610.00015v1","tags":["math.DG","math.MG","cs.DM","msc:05B45","msc:52C20","msc:05A15","msc:52B20","msc:11B83","OEIS A391498","lattice trapezoids"],"score":0,"title":"Tilings of an equilateral triangle by at most five lattice trapezoids with 60° base angles: a complete structural classification","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Gonzalo Barria"],"reviews":0,"subject":"math.CO","summary":"We study tilings of an equilateral triangle of side n in the triangular grid by k lattice trapezoids with base angles 60°, the objects behind the OEIS sequences A389392 (k = 4) and A391498 (k = 5). We prove two angle identities valid for every such tiling and a lemma relating the number of boundary vertices to the number of pieces having a side on the boundary. With these tools we show that there are exactly 1, 2 and 13 combinatorial types of tilings for k = 3, 4, 5. For k = 3 every tiling is a pinwheel. For k = 4 every tiling belongs to one of the two categories used in A389392, a fact that…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-01","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}