Tilings of the regular N-gon with triangles of angles π/N, π/N, (N-2)π/N for N=5, 8, 10 and 12

We say that a triangle T tiles a polygon A, if A can be dissected into finitely many nonoverlapping triangles similar to T. We are concerned with the question whether the triangle of angles pi /N, pi/N, (N - 2)pi/N tiles the regular N-gon. It is easy to see that if N = 3, 4 or 6, then the answer is affirmative. We show the same in the cases N = 5, 8, 10 and 12. (c) 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).