In this puzzle, solvers must deduce how to extract 24 6-letter words from the first image of 24 non-intersecting (but sometimes abutting) triangles.
Each triangle's vertices can be transformed to an integral grid range of values [0,25] corresponding to letters ['A','Z'].
Vertices could be converted to letter chunks as XY or YX, but YX chunks don't form words (except IRISES->SERISI/SIRISE).
Converting each vertex into an XY chunk, there is a single permutation of the vertices that produces a reasonable word, these are the 24 words:
AUGURY BEADED CHAFED COBRAS DIGGED DINGLE ERASES FENCED FUGUES INDIAN INKING INSULT IRISES LUXURY MINING MINION NABBED PERISH RESCUE ROPING SQUISH SUMMON THRESH UPTOWN
There are some near-miss words some anagrammers may suggest (proper names, locations). Hopefully people didn't get caught up on these: DINGLE>LEDING, INDIAN>DIANIN
The correct 24 6-letter words fit uniquely into the crisscross provided.
Reading top to bottom, left to right the marked letters, you get the answer phrase PASSIONISTHEGENESISOF
The conclusion of the quote is the answer: GENIUS
The identified triangles:
The crisscross solution: