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An infinite amount. It starts:

Point

Line

Triangle - 3 sides

Square - 4 sides

Pentagon - 5 sides

Hexagon - 6 sides

Heptagon - 7 sides

Octagon - 8 sides

Nonagon - 9 sides

Decagon - 10 sides

Hendacagon -11 sides

Dodecagon - 12 sides

.... Hectogon - 100 sides

.... Chiliagon - 1,000 sides

.... Myriagon - 10,000 sides

.... Hecatommyriagon - 1,000,000 sides

The list never ends.

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Q: How many plane shapes do you have?
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