Symmetries and frieze groups mathematically capture design pattern properties.

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• Local symmetries act as a kind of glue which holds space together; the more glue there is, the more the space is one, solid, unified, coherent—and the symmetrical segments must overlap for the glue to be effectiveclaim0.778
  Interpretation of the experimental finding: overlapping local symmetries are the hidden structural feature that creates perceived wholeness
• Seven frieze pattern groupsframework0.778
  Classification of one-dimensional periodic patterns into 7 symmetry groups using international notation pxyz
• Approximate calculations with symmetries gave accurate experimental results for architectural wholeness (Book 1, appendix 6).finding0.765
  Empirical validation of the theory of centers in architecture.
• A true collective pattern language will almost always contain the fifteen properties as transformations, and they will be implicit in the geometry of the patternsclaim0.761
  Connection between the deep structure of the vision and the fifteen properties of living structure
• Seven Frieze Symmetry Groupsframework0.760
  Mathematical classification system for one-dimensional periodic patterns using group theory; core framework for the analysis.
• Frieze Patternsconcept0.754
  The primary mathematical object of study; one-dimensional infinitely-repeating geometric patterns found in Islamic art.
• Determining whether or not a pattern has glide-reflection symmetry can be challengingclaim0.753
  Author's methodological note about subtlety of glide-reflections
• Local symmetries are pervasive in nature (sun, trees, crystals, bodies) and are associated with minimum energy and least-action principles.claim0.744