Aegenus proved the existence of the triangle by merging two circles, thereby demonstrating the marriage between the line and the curve. This was the First Rule, the primary geometric lesson that informed the world.
Xernbawe believed the line was stronger than the curve, and his stamp, unlike his brother's, was two triangles. One looked up; one looked down.
The architects who took up the trowel and the compass believe the upward-looking triangle is symbolic of man's upright nature; the downward-pointing triangle is the power that hangs from his hips, the plumb that anchors him to the world.
Before the Tower was built, Ghen's masons were banished from Babylon. Their methods and practices were declared heretical, and the penalty for building in the style of the third brother was a bludgeoning death.
The brethren of Ghen no longer touch iron or steel, but they still build and shape. This is not an impossibility, but an incongruity of language.
Much like Ghen himself, the brother who believed in neither the primacy of the curve nor the supremacy of the line.