Here's my post on
Indian Head cent History. Some well known, some not. Some any old person can find on Wikipedia, some not

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I figured we have all ranges of numismatics reading, so I'll go from basic / well known to more peculiar.
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The 'Indian Head' nickname is from the headdress worn by Lady Liberty on the obverse. So more correctly it's 'Liberty with Feather Headdress' Cent. Indian Head works just as well

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The Union Shield was added to the reverse after the start of the Civil War in 1860 only 1 year into the new Indian Head design.
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Indian Head cents were the first
US coins to be made of Nickel, and were the first to have the nickname 'Nickels'.
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The original composition of Indian Heads being Nickel, they were hoarded during the civil war along with most silver coins making coinage scarce. This is the reason for all the copper Civil War tokens being produced privately as an alternative to US Mint coins. Copper tokens were so successful the mint changed over Indian Heads to that composition when the War ended in 1864.
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The
Indian Head cent replaced the Flying Eagle after only 2 years because the die cast design for FE placed pressure in all the wrong places, making for weak strikes, or broken dies in such a hard metal (Nickel). The Indian head had a centered head obverse balancing the pressures of the relative void of the wreath on the reverse making it a winning combination. However, the switch to softer copper only 5 years later would have also solved the problem.
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Why is Liberty on almost all classic coinage including the 'Indian Head'? When the US Mint was first established, George Washington and others strongly outlined that ideals, not men should be featured on coinage, so much that they wrote it very specifically into law that LIBERTY would be depicted on all coinage. Lincoln was the first 'Man' to appear on
US coinage when the Indian Head was replaced in 1909. Although Presidents grace most our coins today, no living person has been featured on a US Regular Issue coin....yet.