Abraham Lincoln
Susan B. Anthony, Statue of Liberty, Sacajawea
Most of the faces on coins are important figures in history. Some of these figures are George Washington on the quarter, Abraham Lincoln on the penny, Thomas Jefferson on the nickel, Sacajawea on the gold dollar, and Franklin Roosevelt is on the dime.
The best thing to do is click on images on you browser and type in US Coins, this will bring up pictures of US coins
Stamping shapes on coins is less detailed & harder to do
Abraham Lincoln
Susan B. Anthony, Statue of Liberty, Sacajawea
Coins have faces on them to honor that person , statesmen , or president , and they symbolize the country that they were issued by.
ben franklin Patrick Henry
The Lincoln penny of 1909 was the first US coin with a president's face on it.
The patterns on coinage are made by squeezing the coins metal blank between the faces of two hard presses into which the negative of the coins faces have been etched (called dies).
The US Congress passed a law that ordered the US mint to issue these coins. The plan was to get people to use the one-dollar coins in place of the paper dollar bills and save millions in replacement costs. ( I do not know which Congressmen or senators pushed for the law.)
The value of coins comes from how old they are, the condition, and the metal they are made from. Some older coins have different faces because the leaders of countries change over time.
I am guessing you are thinking of Mt. Rushmore . You could also be thinking of coins and paper money and older US stamps.
The US Mint produces circulating coins, commemorative coins, and bullion coins for the United States.
Queen Elizabeth II faces to the right on British coins. Traditionally, kings and queens alternate the direction they face on British (and most Commonwealth) coins. King George VI (1937-1952) faces to the left. King Edward VIII (1936) broke tradition and faced left, but his coins were never issued in Britain. King George V (1911-1936) faces to the left. King Edward VII (1902-1910) faces to the right. Queen Victoria (1838-1901) faces to the left. King William IV (1830-1837) faces to the right. King George IV (1820-1830) faces to the left. King George III (1760-1820) faces to the right. King George II (1727-1760) faces to the left. King George I (1714-1727) faces to the right. Queen Anne (1702-1714) faces to the left. etc.
Ancient Greek coins often had the faces of Kings/Gods/Goddesses/famous people on them.