More information that I have found on the Hesselberg triangle.
The Saris reference shows a photo of a Hesselberg triangle that looks like a good period example, and has a traditionslitzen on page 409. In his list of AHS schools he states the following.
'It is not known to what extent triangles were actually worn. It is possible they were manufactured for use and mostly kept in stock by some of the schools, to be used when that school did indeed open. This is probably the reason why so many triangles in collections today are in new condition. The war obviously derailed the opening of some schools.'
He states in the photo caption for the Hesselberg triangle that students that were to attend this location were housed at the Ordensburg Vogelsang.
He states his sources as:
Scholtz pp 208-209, from the Kurzes Kalendar 1942.
Die Adolf Hitler Schule 1937
Berliner Borsenzeitung dated April 20, 1937.