#truncation

Hi there.

Im glad you like my shape. (Although I dont know which of my shapes you mean exactly.)

Nevertheless, Im excited you are curios about truncation.

You got this part right that the square turns into a polygon with differnt properties.

Truncation is method where you cut off the vertices of a polygon or polyhedron, so to speak. (A polygon is 2-dimensional. And a polyhedron is 3-dimensional.)

Truncating a square: Cut off the four vertices to less than half of the edge's length. This results in an octagon:

Or cut off the four vertices to exactly half the edge's length and you get a smaller square:

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Cutting off the vertices of a polyhedron is similar.

If we start with a cube and cut off all of the eight vertices of the cube, the six square faces will turn into octagons, and the vertices will turn into triangles, because three faces of the cube meet per each vertex. This results in the truncated cube that has six octagons and eight triangles.

Alternatively we can just increase the cut-off, and cut off the vertices of the cube up to half of the edge length: This results in the cubocahedron with six squares and eight triangles.

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You could experiment/test/visualize this with a cheese or play-doh.

By cutting off the vertices of the dodecahedron you get the truncated dodecahedron.

This results in the 12 pentagonal faces of the dodecahedron turning into 12 dekagonal (10-gonal) and 20 triangular faces.