The angles of the original triangle were oblique and created more of a distorted quadrilateral.

This creates 12 new pentagon faces, and leaves the original 20 triangle faces as regular hexagons.

Therefore, the angle between the side of lengths a and b in the original triangle is a right angle.

The intersection inside the original triangle between the two circles is the Fermat point.

In the end, we get a shape looking somewhat like a tree, but with an area much smaller than our original triangle.

Expressed in terms of the side length s of the original triangle this is .

The difference in area of these two triangles equals the area of the original triangle.

The perimeter of this figure is 4:3 longer than the original triangle.

The nine-point circle created for that orthocentric system is the circumcircle of the original triangle.

The feet of the altitudes in the orthocentric system are the vertices of the original triangle.