It is well known that the crystallography of approximants is directly relat
ed to that of the parent quasicrystal, once its unit-cell vectors are ident
ified as parallel projections of certain N-dimensional lattice nodes A(i).
Derived here are explicit simple relations for calculating the shear matric
es epsilon and the related crystallographic properties of the corresponding
approximants, including diffraction indexing and the determination of the
lattice in perpendicular space. Applied to low-dimensional approximants, th
e derivation shows that the systematic 'accidental' extinction rules observ
ed in the pentagonal phases are generic extinctions that are due to the geo
metrical properties of the projected 1D lattice and are independent of the
actual model of the quasicrystal.