It is easy to note that an equilateral triangle can be cut into 3 mutually congruent and non-convex polygons *(replace the 3 lines meeting at centroid and separating out the 3 congruent quadrilaterals with identical polylines to get 3 congruent, non-convex pieces)* and this partition is easily generalized to 12, 27, ... number of pieces.

* Question*: Are there other triangles that can be cut into N polygons that are

*and mutually congruent? If so, for what values of N?*

**non-convex*** Note 1*: I don't know if there is any partition of any triangle into 7 mutually congruent polygons, convex or otherwise - although it has been proved (https://arxiv.org/pdf/1811.09723.pdf) that no triangle can be cut into 7 or 11

*.*

**congruent triangles*** Note 2*: It is known that there are convex polygons that can be cut into a finite number of non-convex and mutually congruent pieces but NOT into convex congruent pieces (eg: A claim on partitioning a convex planar region into congruent pieces).