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Edwina Ellis, who designed the coin, said: "He made difficult subjects accessible and engaging - that's what I wanted to portray.
"Hawking, at his playful best, invites the audience to contemplate peering into a black hole before diving in. I wanted to fit a big black hole on the tiny coin and wish he was still here chortling at the thought."
Hawking's son and daughter, Tim and Lucy, were present at the Royal Mint for the unveiling of the coin celebrating their father.
Lucy said: "I hope my father would be pleased to be alongside Sir Isaac Newton and Charles Darwin as scientists who have made it onto money!"
The coin has been so popular since it was unveiled, the Royal Mint's website is now struggling to cope with the demand.
All versions of the coin have been reserved, apart from the standard option.
A message on the site says: "Due to the popularity of this launch, our website is still experiencing high volumes of traffic but we have a queue system in place to get you onto our site as quickly as possible.
"Thank you for your patience. Please do not hit refresh or reload this page as it will increase your wait time."
The English theoretical physicist, cosmologist and author died peacefully at his home in Cambridge in the early hours of Wednesday 14 March, at the age of 76.
Hawking, who battled motor neurone disease and had only been given a few years to live in his twenties, was renowned around the world for his incredible genius but also for his ability to make people laugh, which increased his immense popularity and respect.
Tributes poured in for Hawking at the time of his death, showing how widely he was respected around the world.
A spokesperson for NASA said: "Remembering Stephen Hawking, a renowned physicist and ambassador of science. His theories unlocked a universe of possibilities that we & the world are exploring. May you keep flying like superman in microgravity, as you said to astronauts on @Space_Station in 2014."
As well as his work in the scientific community, he also crossed over into popular culture as a result of his success in science and huge reputation, making memorable appearances in TV shows such as The Big Bang Theory and The Simpsons. He was also the subject of the Oscar-winning movie, The Theory of Everything.
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