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1859 1C Indian Cent--Obv. Struck on 1857 Half Dime
Photos and Copy used with permission and courtesy of Heritage Auction Galleries
Two years after it was minted, an 1857 half dime became mixed with blank planchets ready for production of 1859 Indian cents. During the coinage process, this half dime was fed into the press on top of a blank cent planchet, and the two pieces were struck together. The result was the obverse overstrike with the Indian cent impression over the half dime obverse, and the wavy and somewhat flattened half dime reverse.

It is also fascinating to ponder the other coin that was produced in this same operation, essentially an Indian cent with a half dime size indent, consisting specifically of the 1859 Indian cent reverse with nothing but the border dentils and tops of a few letters visible on the obverse.
Apparently unique with no rumor of any other similar examples

This unique error is listed in a few different references including Appendix B of the Judd pattern book (seventh edition edited by Abe Kosoff) where it was described as "1859--CENT. Weakly struck over a half dime, date not showing. Reverse slightly blurred by the overstriking." It is also recorded in the ninth edition of the same reference (edited by Q. David Bowers) where it is included as one of just 14 "Classic Mint Error Specimens."

The two numbers given to this piece by Edgar H. Adams and William H. Woodin in United States Pattern, Trial, and Experimental Pieces carry slightly different descriptions, although there is little doubt that they refer to the same coin. AW-310: "Mule of the obverse of the cent of the year, without date, with the reverse of the half dime of the year." AW-319: "The adopted obverse. Rev. the reverse of the half dime of the year."

Don Taxay recorded this overstrike on page 392 of the 1971 edition of Scott's Comprehensive Catalog and Encyclopedia of U.S. Coins.

More recently, Andrew Pollock listed this coin as P-3188, where he misdescribed it as an obverse die trial: "Struck on the obverse side of a regular-issue 1857 half dime."