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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
Computational Geometry ( IF 0.4 ) Pub Date : 2020-07-21 , DOI: 10.1016/j.comgeo.2020.101690
M. Laczkovich

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 π/N,π/N, (N2)π/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.



中文翻译:

常规的拼接Ñ与角三角形边形π / Ñπ / Ñ(,Ñ  - 2)π / ÑÑ  = 5,8,10和12

我们说一个三角形牛逼瓷砖的多边形一个,如果一个可以被分成有限多个不重叠的三角形相似牛逼。我们关心的是角度三角形π/ñπ/ññ-2π/ñ平铺常规N -gon。

很容易看出 ñ=34或6,则答案是肯定的。我们在情况下也显示相同ñ=5810 和12。

更新日期:2020-07-21
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