Doubly-true dissections: Dissecting an $n$-gon into $s_i$-gons, such that $n = \sum s_i$

171 Views Asked by At

Dissecting a polygon into other ones is a famous subject. Many people have studied varying topics about dissection.

It is well known that a regular hexagon can be dissected into two equilateral triangles. We can denote this dissection by {3}+{3}={6} by using Schläfli symbols.

We can also dissect a regular octagon into two squares and denote it by {4}+{4}={8}.

The equalities {3}+{3}={6} and {4}+{4}={8} also holds as numbers. If an $n$-gon can be dissected into $s_1$-gon, $s_2$-gon, ..., $s_k$-gon and $n = \sum_{i=1}^k s_i$, then I would like to call this type of dissections ''doubly-true dissections.''

For one more example, we can consider {12} = {4}+{4}+{4}.

Do you have any other doubly-true dissection?

enter image description here