Iron Brigade and was previously called the "Black Hat" Brigade. The 3rd Brigade Combat Team, 1st Infantry Division was known as the Iron Brigade from its formation in 1917 through World War I, World War II and Vietnam, until some time in the early 2000s when, for reasons that are still unclear, the name was changed to Duke Brigade. The unit crest was an Iron Cross in a triangle, it appears that that was also changed. The 3rd Brigade of the 4th Infantry Division is also known as the Iron Brigade. Its unit crest is similar to the medals issued to veterans
Extouch triangle Extouch triangle In geometry, the extouch triangle of a triangle is formed by joining the points at which the three excircles touch the triangle. The vertices of the extouch triangle are given in trilinear coordinates by: or equivalently, where "a,b,c" are the lengths of the sides opposite angles "A, B, C" respectively, The triangle's splitters are lines connecting the vertices of the original triangle to the corresponding vertices of the extouch triangle; they bisect the triangle's perimeter and meet at the Nagel point. This is shown in blue and labelled "N" in the diagram. The Mandart inellipse is tangent to