What points can I use in a designed experiment?

The following table describes different types of points in a designed experiment:
Point Screening Designs Factorial Designs Response Surface Designs Mixture Designs
0 center point center point center point centroid
1 corner point corner point (cube point) cube point (corner point) vertex
-1 - - axial point axial point
2 edge midpoint* - edge midpoint** edge midpoint (double blend)
3 - - - triple blend***

*Applies only to definitive screening designs.

**Applies only to Box-Behnken designs.

***In mixture designs, the point type increases naturally (or respectively) with higher order blends.