I'm having trouble calculating the normal vectors for the four sides of a pyramid. Of course, a pyramid is just 4 separate triangles that share a set of 5 vertices. My four triangles sit at these coordinates:

(0, 0, 0)

(1, 0, 0)

(0.5, 1, -0.5)

(1, 0, 0)

(1, 0, -1)

(0.5, 1, -0.5)

(1, 0, -1)

(0, 0, -1)

(0.5, 1, -0.5)

(0, 0, -1)

(0, 0, 0)

(0.5, 1, -0.5)

When I calculate the normals for each of these triangles, I get the following vectors (in the same order shown above):

(0, 0.5, -1)

(-1, 0.5, 0)

(0, 0.5, 1)

(1, 0.5, 0)

This calculation is for a 3d computer application, but the lighting is clearly off, which tells me that I am getting the wrong answer. Can anyone help me out? Thank you!