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In making the gift, Lady Hillary had been motivated to ensure the items, willed to her by Sir Edmund, made their way into a public collection for long-term preservation and public accessibility, museum officials said.
The gift includes a Kodak Retina camera Sir Edmund used on the summit of Mt Everest to capture the historic ascent in 1953 and one of the best-known photographic portraits of Sir Edmund, given to him by the photographer, Yousuf Karsh, a Canadian of Armenian descent.
Other items include a well-known Hillary mug, from the Everest expedition, rock shards Sir Edmund collected as a memento atop Mt Everest.
Another item is an ice axe used on the 1956 Trans-Antarctic expedition.
In a statement, Lady Hillary said she was "very confident" the museum would "care for these items appropriately as their custodians for all New Zealanders".
"And I know they'll display them with pride as reminders of Ed," she said.
Museum officials said the gift would be displayed "in the heart of the museum", in the atrium foyer and stairwell.
The artefacts would be "visible to all who visit the museum".
The exhibition will be opened by Lady Hillary this evening.
Museum chief executive Shimrath Paul said the Dunedin and Otago community would take "enormous pleasure and inspiration from these significant items"Museum staff were honoured that Lady Hillary had chosen the museum to receive the gift, he said.
"We welcome visitors from New Zealand and beyond to share with us in this.
"Sir Edmund's story reminds all of us of what it is to be a New Zealander," Mr Paul said.