Below is part of a library of PascGalois triangles to supliment the images found in
The PascGalois Triangle: A Tool For Visualizing Abstract Algebra - Bardzell & Shannon

Click on an image to enlarge it. In recent versions of browsers, you should get a caption for each picture when your mouse points to it. Beacuse of the limitations regarding subscripts in these captions, the notation used is not PG(a,b) but rather G(a,b) to refer to the PascGalois triangle using group multiplication from the group G and generators a and b. In D5, D6and D8 the identity is purple, rotations are blue & green and relections are red/orange/yellow/pink . . .


D3, D4, D5, D6 and D8. Dihedral Groups of the symetries of regular 3,4,5,6, and 8 sided polygons


D3
d3(rotation, reflection) with 16 rows d3(rotation, reflection) with 32 rows d3(rotation, reflection) with 64 rows d3(rotation, reflection) with 128 rows d3(rotation, reflection) with 256 rows
D4
d4(rotation, reflection) with 16 rows d4(rotation, reflection) with 32 rows d4(rotation, reflection) with 64 rows d4(rotation, reflection) with 128 rows d4(rotation, reflection) with 256 rows
D5
d5(rotation, reflection) with 16 rows d5(rotation, reflection) with 32 rows d5(rotation, reflection) with 64 rows d5(rotation, reflection) with 128 rows d5(rotation, reflection) with 256 rows
D6
d6(rotation, reflection) with 16 rows d6(rotation, reflection) with 32 rows d6(rotation, reflection) with 64 rows d6(rotation, reflection) with 128 rows d6(rotation, reflection) with 256 rows
D8
d8(rotation, reflection) with 16 rows d8(rotation, reflection) with 32 rows d8(rotation, reflection) with 64 rows d8(rotation, reflection) with 128 rows d8(rotation, reflection) with 256 rows