Further Questions about Tetrads
11. Can two tiles of a Tetrad form a regular polygon?

Odd number of edges
As n-gons with odd n are not point symmetric, the two tiles which form the n-gon have be mirror images of one another. But as the tiles cannot be convex there has to be a hole in the n-gon. The whole tetrad has at least two holes.

Even number of edges
Two tiles form a n-gon with a point symmetric structure of the dissection lines. The shape of the whole tetrad is mirror symmetric and has no holes. For each even n there are two essentially different ways: the two tiles outside the n-gon touch in the middle of an edge or in a vertex of the n-gon (see n = 4)

n = 3   Triangle

n = 4   Square

n = 5   Pentagon

n = 6   Hexagon

n = 7   Heptagon

n = 8   Octagon

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 Walter Trump, Nürnberg, Germany, ms(at)trump.de, © 2020-02-12 (last modified: 2020-02-12)