Trisecting the sides of a polygon
A Truncation is an operation applied to a polyhedron. Using this applet, you can explore the dividing sides of a polygon into 3 unequal parts: t, 1-2*t, t where 0<t<0.5. I have used this method to construct truncated polyhedra.
In the following applets, you can explore polyhedra at various stages of truncation.
Truncated Tetrahedron.
Truncated Cube.
Truncated Octahedron.
Truncated Dodecahedron.
Truncated Icosahedron.
Truncated square antiprism
Truncated Cuboctahedron.
Truncated Icosidodecahedron.
Truncated Biscribed Pentakis Dodecahedron.
Drag the slider t to show the truncation the sides of the n-gon.