Pyramid.
Or triangular prism, depending on what exactly you mean.
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What is a pyramid
There is not such thing as a three-dimensional triangle. You are thinking of a tetrahedron which is a three-dimensional figure with each side being a triangle. This has four vertices.
No. A triangle can be a two-dimensional object whereas a pyramid must be three-dimensional (with sides that are sloped).
Tetrahedron
it can be three dimensional. a polygon is three sided or more like a triangle. so to answer your question, yes.