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Man With a Plan: Minoru Yamasaki

American architect Minoru Yamasaki designed the towers, whose narrow vertical windows -- heavily influenced by Gothic architecture -- helped humanize (barely) the towers' sleek, minimalist look and feel. Interestingly, the man who envisioned New York's tallest buildings had a fear of heights. Photo: Stan Wayman/Time & Life Pictures/Getty Images

For the full photo collection, go to LIFE.com

Building the Twin Towers

When terrorists flew planes into both Twin Towers on a crystal clear September day in 2001, horror mingled with disbelief and, even in the midst of the chaos, with rage. No one who saw the towers fall will ever forget it. But as time passed, the sight of a skyline without the Twin Towers became more than just a reminder of a savage attack and the loss of thousands of lives. It also brought home to New Yorkers -- and to millions of others around the world -- that they'd somehow grown improbably fond of the two severe, oddly companionable monoliths anchoring Lower Manhattan. Here, LIFE.com pays tribute to those engineering marvels ...