## PascGalois Triangles for Some of the Dihedral Groups

 D3 PascGalois Triangle D4 PascGalois Triangle D5 PascGalois Triangle D6 PascGalois Triangle D7 PascGalois Triangle D8 PascGalois Triangle
All of these triangles were produced by placing a rotation though 360/n degrees down the right side of the triangle and a flip down the left. We leave it as an exercise for the reader to verify that repeated multiplication of these two elements will generate the entire group for all n. This is the standard construction we will use for PascGalois Triangles for Dn throughout this paper. Would you like to see them in different colors?

You may notice that D4 and D8 have much more easily discernable patterns than the others. Unfortunately, the reason for this is beyond the scope of this paper. However, if we change the coloring scheme so that all the rotations are colored blue/green and the flips are colored red/purple, see what happens:
 D3 PascGalois Triangle D4 PascGalois Triangle D5 PascGalois Triangle D6 PascGalois Triangle D7 PascGalois Triangle D8 PascGalois Triangle

Although the triangles for some are always fuzzier than others (e.g. D4 and D8), all of the triangles exhibit the similarity to the triangle for Z2 when rotations and flips are clearly distinguishable. Again, this happens because when you lump all the flips together as if they were the same element and you lump the reflections together as if they were all the same, the resulting multiplication table is the same as that for Z2 with 0 replaced by the rotations and 1 replaced by the flips.