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We add a little to On partitioning convex polygons into kites

In his answer to above post, Tom Sirgedas has shown that a convex polygon having two successive angles acute or right is a sufficient condition that the polygon cannot be partitioned into obtuse kites. It is not clear if the condition is necessary.

  • How does one fully characterise those convex polygons that cannot be partitioned into any finite number of obtuse kites?

Note: another question raised in above linked post - reg partition of convex polygons into acute kites remains open as far as I know.

Further remark: One wonders what could be said regarding partition of polygons into kites in non Euclidean geometries

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  • $\begingroup$ What is so special about kites? Perhaps investigating what happens for different types of convex quadrilaterals might be insightful. There is a sense based on ideas of Branko Grunbaum that there are 21 different types of convex quadrilaterals. So one can generalize the spirit of the question posed here. See this paper for a discussion and extensions of Grunbaum’s approach: jstor.org/stable/10.5951/mathteacher.106.7.0541 $\endgroup$ Commented Sep 4 at 18:25
  • $\begingroup$ Thanks for this interesting link. As to how kites could be interesting, any polygon can easily be cut into finitely many right kites and so right kites may be in some sense special as opposed to acute and obtuse ones - at least in Euclidean geometry $\endgroup$ Commented Sep 5 at 4:32
  • $\begingroup$ Moreover, it appears that kites are among quadrilaterals what isosceles triangles are among triangles $\endgroup$ Commented Sep 5 at 8:23

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