Six.
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First, I'm assuming the by corners, you mean verticies. Second, the answer depends on what you mean by "three dimensional triangle. To some, this could be interpreted as a pyramid. However, I think it is more likely that you are referring to a triangular prism- a prism shape with a triangle as each base. In this case, there are six "corners". Each side has three, where the length-wise edges of the prism intersect the verticies of the triangle. There are three corners on each side, for a total of six. If you really meant a pyramid, then there are five corners.
A triangular prism has six vertices (corners).
A rectangular prism (or cuboid) has 8 corners.
A rectangular prism has 8 vertices/corners.
A rectangular prism has 8 vertices (corners), 6 faces.