Summary

There are two problems with the original design:

1. the distances between the center peg and the other two pegs are not equal
2. the pegs are two thick. Holes punched with a standard 3-hole punch do not fit

So, I redesigned it from scratch with the following change:

1. distance between two pegs is 4.25" or 108mm,
2. diameter of pegs is reduced to 5mm, 1mm less than the holes produced by hole punch (0.25" or 6mm).