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"Vertices" means corners.
"Tetra" means four and "hedron" means side, so a tetrahedron is a four sided object. A tetrahedron looks like pyramid. Each side is a triangle.
The bottom of a tetrahedron is a triangle, and a tetrahedron goes up to a point at the top. The three corners of the triangle at the bottom plus the point at the top gives you a total of four corners.
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