The two hi-tech behemoths went to court over the designs that have now become commonplace on most popular smartphones, with a court ruling in 2012 in favor of Apple.
At issue were design features by now familiar to consumers: a black, rectangular, round-cornered phone front, a surrounding rim, known as the "bezel" and a grid of 16 colorful icons.
Those design elements were protected, prompting the jury to award Apple all the profits from sales of smartphones containing those features, Samsung lawyers said in their filing.
"While Samsung prefers to compete in the marketplace, not the courtroom, the company feels that it is important to appeal this case to the US Supreme Court on behalf of all US companies, big and small, that could be affected if this legal precedent stands," the company said in an email response to an AFP inquiry.
Several of the world's technology titans filed briefs supporting Samsung while the case was in federal circuit court in Silicon Valley, according to the firm.
Attorneys for the South Korean consumer electronics titan argued that the massive payout was not warranted, because smartphones "contain countless other features that give them remarkable functionality wholely unrelated to their design."
"Even if the patented features contributed one percent of the value of Samsung's phones, Apple gets 100 percent of Samsung's profits," the appeal said.
In response to an AFP inquiry, Apple said it stands by its comment after the trial victory in 2012.
"The lawsuits between Apple and Samsung were about much more than patents or money," the Apple statement said.
"They were about values. We applaud the court for finding Samsung's behavior willful and for sending a loud and clear message that stealing isn't right."
Samsung pays up
Samsung early this month agreed to pay smartphone rival Apple just over $548 million (roughly Rs. 3,672 crores) in the years-long patent battle in federal court in California.
However, the agreement came with one key proviso, as the two tech giants agreed to continue "to pursue the existing cases in US courts."
Samsung said in a legal filing that it would pay Apple the partial judgement awarded but that it reserved the right to get money back if the amount is modified or overturned on appeal or if the validity of patents at issue is successfully challenged.
Apple said in the joint filing that it disagrees with Samsung's contention that it has a right to be reimbursed.
A court in September awarded Apple the partial judgment. Samsung's options narrowed to simply paying the money or trying to take its fight to the US Supreme Court.
The hefty sum is significantly less than the billion dollars Apple sought at the outset of the 2012 patent trial in Northern California, and doesn't put to rest an argument over who should pay Apple's legal costs said to total $1.8 million (roughly Rs. 12 crores).
In another sign that the legal fight would drag on, Apple also asked the court for a green light to file a motion asking for supplemental damages for products that weren't calculated into the award.
Samsung and Apple decided last year to drop all patent disputes outside the United States, marking a partial ceasefire in a long-running legal war between the world's two largest smartphone makers.
The arch-rivals have battled in close to a dozen countries, with each accusing the other of infringing on various patents related to their flagship smartphone and tablet products.
But neither has managed to deliver a knock-out blow with a number of rulings going different ways, and in an announcement they agreed to drop all litigation outside the United States, suggesting a line was finally being drawn.
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