The battle between Apple and its rival Samsung over the design of the iPhone would he heard in the US Supreme Court on Tuesday.

The court will decide how much the South Korean smartphone giant should have to pay its rival Apple (AAPL) as financial damages, for copying the iPhone's design and allegedly violating design patents. The US Supreme Court will hear the long-running legal battle on Tuesday.

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The conflict has drawn the attention of over a dozen amicus curiae ("friend of the Court" briefs) who are watching the case closely as the ruling would have wide-ranging implications on balancing technological innovation and preserving intellectual capital.

Some of those briefs came from influential tech firms including Facebook (FB), Google (GOOG, GOOGL), Dell and Hewlett-Packard (HPQ), which said the dispute "presented a question of enormous practical importance" to them.

This is the first time the US Supreme Court has taken up a design patents case in more than a century, four years after The US Court of Appeals for the Federal Circuit jury found that Samsung had copied part of the iPhone's design, distinctive front screen, and graphical touchscreen user interface. The court awarded Apple almost $1 billion in damaged, but it was later decreased to $548 million.

According to Apple, Samsung mimicked elements of the iPhone's design including its rounded edges, a "bezel" or enclosing rim, a network of 16 vivid icons and the phone's "distinctive display" among other features.

California-based Apple had protected those characteristics of the iPhone with US design patents.

A verdict is expected to be announced in the coming months. Rather than deciding the matter of violation, the Supreme Court will determine if Samsung owes Apple all the earnings it made from producing copycats of its groundbreaking smartphone or only those profits attributable to the infringing features.