There is a box next to one of the oval office table lamps, with a gold seal on the top. Maybe anons can find a better pic.
Speaking of JFK, look closely what he had on his desk. The glass paperweight, could be the same coin, or could be just an homage from Trump.
Items on the desk
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Black Alligator Desk Set
Six pieces: Desk Pad; Holder for Paper Clips and Pencils; Note Pad; Rocker Blotter; Blotter holder; Cigarette Holder; Letter Sorter.
Gift from President Charles de Gaulle of France, on the occasion of President Kennedy's state visit to Paris, June 1961.
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Presidential Appointments Schedule for Thursday, November 21, 1963
Shows the following appointments:
9:30 AM Hon. Thomas S. Estes, U.S. Ambassador to Upper Volta.*
Hon. Charles F. Darlington, U.S. Ambassador to the Republic of Gabon.*
10:50 AM Depart South Lawn for TEXAS
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Coconut Shell, Encased in Plastic
Although now obscured by the clouded and scratched plastic which encases it, the coconut husk bears the inscribed message:
NAURO ISL NATIVE KNOWS POSIT HE CAN PILOT
11 ALIVE NEED SMALL BOAT KENNEDY
The message was inscribed by Lt(jg) John F. Kennedy after his PT Boat, PT 109, was rammed and sunk by a Japanese destroyer, the AMAGIRI, and he and his men were marooned on Nauro Island in the Solomons in World War II. (1)
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Book-ends
The book-ends on the desk are replicas of cannon mounted on the U.S.S. CONSTITUTION ("Old Ironsides"), now berthed in Charlestown. See also article on artist.
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Plaque Inscribed With the Breton Fishermen's Prayer
"O, God, Thy sea is so great, and my boat is so small."
Presented to President Kennedy by Vice Admiral Hyman G. Rickover, "Father of the Nuclear Navy."
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Steuben Glass Etching
The etchings are of a PT boat and the Presidential seal. The item was presented to President Kennedy by an organization of PT Boat veterans known as Peter-Tare, Inc.
7. Gold Inaugural Medal
The medal commemorating his inauguration was presented to President Kennedy by the Inaugural Committee.
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Ashtray
The ashtray is of Waterford crystal and bears an etching of the Kennedy coat-of-arms. The ashtray was presented to President Kennedy by Mrs. Dorothy Tubridy of Dublin, Ireland.
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Books
Among the books that President Kennedy habitually kept on his desk were the following:
a. Leather-bound copies of his own publications:
As We Remember Joe (personal reminiscences of his brother, who was killed in World War II)
Strategy of Peace
Profiles in Courage (his Pulitzer Prize winning work of biography)
To Turn the Tide
Why England Slept (his honors thesis for Harvard University)
b. Other publications:
The speeches of JFK during the 1960 Campaign
Joint Appearances of Senator Kennedy and Vice President Nixon during Presidential Campaign of 1960
Winston Churchill's four-volume biography of Marlborough
Samuel Flagg Bemis's two-volume study of John Quincy Adams
Herbert Agar's The Price of Union
Henri-Beyle Stendahl's The Red and the Black
c. Also on the desk was a pocket Congressional Directory for the year 1963.
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Telephones
One large green telephone with several buttons. Two small black telephones for communicating with his staff and the Mansion. (3)
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Other Items
Magnifying glass (5" x 2"), letter opener, framed photographs of his children, an ashtray with JFK's fingerprints on it (apparently a gift from J. Edgar Hoover, Director of the Federal Bureau of Investigation), a wooden handle with the die of the Presidential seal, a lamp, and ink and pen holders.
According to a response written on 27 February 1961 by Pierre Salinger, Press Secretary to President Kennedy, located in the White House Central Subject File here at the Kennedy Library, the lamp was a Hercolite Executive (no. 605SB) made by Herco Art Manufacturing of Wallingford, Connecticut. (4)