No, there are many different types of pyramids.
To give a real-life comparison, the Egyptian pyramids are square pyramids, and have 5 faces.
Triangular pyramids have 4 faces. (Count the base as one face)
A pentagonal pyramid would have 6 faces. (Five on each side, plus the base)
A hexagonal pyramid would have 7 faces, etc.
(One for each side base + the base's face)
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