Mermin replies: I’m glad that Ted Janssen sees some elegance in the approach to crystal symmetry that my collaborators and I developed for aperiodic crystals, and I’m pleased to return the compliment to the standard approach of him and his collaborators.

As far as I know, the precise connection was only recently spelled out between our phase (gauge) functions and the rather different phases (factor systems) that appear in the venerable theory of space-group representations. 1 This link offers a more direct and elementary route from crystal symmetry to some of the major physical applications of space-group representations. 2  

1.
A.
Koenig
,
N. D.
Mermin
,
Phys. Rev. B
56
,
13607
(
1997
) .
2.
A.
Koenig
,
N. D.
Mermin
,
Am. J. Phys.
68
,
525
(
2000
) .