A triangular prism has six vertices. In order to calculate the number of vertices on any type of prism, take the number of corners on one side and multiply by two. For example, a rectangular prism has eight vertices, or two sets of four.
Some other characteristics of a triangular prism are that they have five faces and nine edges. For comparison, a rectangular prism has six faces and 12 edges. Mathematicians have derived Euler's formula for these and similar shapes. It states that for a polyhedron the number of faces plus the number of vertices minus the number of edges is always two. For a triangular prism, this formula holds true: (5 + 6 - 9 = 2).