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Indeed as in the first step of the process there are two types of tile in building ''P''<sub>''n''</sub> from ''P''<sub>''n'' – 1</sub>, those attached to an edge of ''P''<sub>''n'' – 1</sub> and those attached to a single vertex. Similarly there are two types of vertex, one in which two new tiles meet and those in which three tiles meet. So provided that no tiles overlap, the previous argument shows that angles at vertices do not exceed {{pi}} and hence that ''P''<sub>''n''</sub> is a convex polygon.
To see how to handle the case when
:<math>{1\over a} + {1\over b} + {1\over c} < 1</math>
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