Why does the iconic Coke bottle have such an odd shape?

As a child in England I never encountered Coca-cola till I was allowed to visit my father’s office with him on a Saturday and visit the little café at the bottom of the building, where they had ice cold Coke - something hardly known in England at the time (1950s)
It was a massive hit that still sticks in memory. The combination of ice cold liquid, carbon dioxide and the acidic and bitter-sweet liquid was like nothing I had ever encountered before. But once I became an adult, the only time I ever drank it was in a wayside tent café in Mexico - ice cold, ridiculously cheap, and I was instantly eight again in a small café full of lawyers.