who designed it?
John Forsyth.
1804 dollar
He also directed Moore to have two Morocco leather boxes made to house the coins. He stated that one should be yellow in color, and the other crimson, and that funds could be drawn from the Treasury for the value of the boxes and coins. Later, in a letter dated December 2, 1834, Forsyth directed Moore to include "national emblems" (including an eagle and stars) on the exterior of the cases.

In their book "The Fantastic 1804 Dollar", numismatic historians Eric P. Newman and Kenneth E. Bressett assert that a problem arose at the Mint as to how to interpret Forsyth's order. As his initial correspondence indicated that the sets were to include coins of every type then in use,
which country is the 1804 dollar associated with? The United States of America. was it a coin or a note? A dollar coin. what metal was this made up of? Silver.
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1804 dollar [SEP] Edmund Roberts' diplomatic mission
Roberts died in Macau on June 12, 1836, before he could initiate contact with any other nations. On June 30, Edmund P. Kennedy, commodore of the diplomatic fleet, wrote to the State Department that he had "directed that the presents [which remained ungifted due to Roberts' death] be forwarded to the United States". The proof sets meant for Cochin-China and Japan were likely included in the shipment of returned presents. All dollars struck for inclusion in the diplomatic gift sets were likely dated 1804. It is unknown why that date was chosen for the dollars, but numismatic historian R.W. Julian suggests that it could have been done to prevent angering collectors who would not have been able to acquire the 1834-dated coin for their collections; Chief Coiner Adam Eckfeldt, after consulting with Moore, mistakenly determined that 19,570 dollars bearing the date 1804 were struck in that year.