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Southern District Police issued a public statement today asking for help finding the thief, a man calling himself George.
He visited Otago Coin International, Mosgiel, on August 22 to sell coins and purchase a gold sovereign.
The collector, Johnny Lindsay, and "George'' spent about an hour discussing coins and the collector showed him a variety of gold coins.
When the collector's attention was shifted "George'' grabbed the coin collection and ran out the door, police said.
Mr Lindsay said it was "George's" second visit and he had begun to like and trust him.
While police said the man had extensive knowledge of coins, Mr Lindsay said that was not true, describing the thief as "ignorant" but interested.
"I mentioned Julius Caesar but he'd never heard of Julius Caesar - that surprised me," he said.
Before taking the coins the thief appeared anxious and started trembling, Mr Lindsay said.
"I thought he was nervous because he was buying a gold coin from me," he said.
The offender was last seen riding a mountain bike eastward on Church St, Mosgiel.
He is aged between 25-35 years, of slight build and between 167 and 170cm tall.
He had short dark hair and was unshaven.
He was wearing an orange, sleeveless high-vis vest with a dark-coloured jersey and trousers as well as a black beanie and gloves.
Police believe the man lived in Dunedin or Mosgiel and was interested in coin collecting.
"Now that some time has passed he may have shown someone the collection.''
The coin collection featured 45 gold coins, each in a plastic sleeve with a description.
The coins were in a rectangular blue case and were dated between 1700-1900 from the USA, Austria, the Netherlands, France, England, India, Colombia, Spain, Denmark, and Sweden.
The collection also includes 1870 Sydney sovereigns.
They were collected over a lifetime and were of "significant monetary and sentimental value".
If "George'' wanted to set things right he should return the coins to the Mosgiel or Dunedin police station, police said.
If anyone could assist they should call Dunedin Police on (03) 471 4800 or Crimestoppers anonymously on 0800 555 111, quoting file number 180823/2533.