e-mail :
Sequel to Group Theory
As always, we start with reminding the reader about the "Important Remark" near the end of Part III of Group Theory (To see it, click HERE and then go to (end of) Part III ), a Remark concerning the direction of reading products of group elements, like, say, apq. We read such products (from that Remark onwards) from back to front. Thus (with respect to apq) first q, then p, and then a.
Infinite two-dimensional periodic patterns, or Ornaments (sequel)
Sequel to the Plane Group P4mm
In the previous three documents we have analysed a P4mm / P4gm antisymmetry pattern, derived from a square tiling, depicted in Figure 3a of Part XXXVII . Now we will discuss an example of an antisymmetry pattern derivable from a P4mm symmetry pattern, and found in Neolithic art.
e-mail :
I did not finish the present sequence, and may be, I never will (because I turned to other issues [see next LINK ] that are important for developing a metaphysics in the sense of a general ontology [study of Being and Essence of things] ), but the reader has now acquired enough knowledge, I think, to finish this sequence on symmetry by himself if he or she wishes to do so. If that has been done, he or she can turn to the study of the symmetry and structure of three-dimensional crystals, real crystals that is, involving space-groups. This website has given all the information and preparation to do so. Have fun.
But the reader can also move on to Third Part of Website by the following this LINK .
Back to 3-dimensional crystals (conclusion), Organic Tectology and Promorphology
Back to the Beginning of the present Series on Subpatterns and Subgroups. There : LINK to Part XXVII
Back to Part XXVIII of the present Series
Back to Part XXIX of the present Series
Back to Part XXX of the present Series
Back to Part XXXI of the present Series
Back to Part XXXII of the present Series
Back to Part XXXIII of the present Series
Back to Part XXXIV of the present Series
Back to Part XXXV of the present Series
Back to Part XXXVI of the present Series
Back to Part XXXVII of the present Series
Back to Part XXXVIII of the present Series
Back to Part XXXIX of the present Series