framework
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framework:seven-frieze-symmetry-groupsSeven Frieze Symmetry Groups
Mathematical classification system for one-dimensional periodic patterns using group theory; core framework for the analysis.
Neighborhood — ranked by edge-count
Methods (1)
method
- International Symbol Notation (pxyz)implementsStandardized notation system for describing and classifying the seven frieze pattern groups using letters and numbers.
Concepts (8)
concept
- p111 Frieze Patternassociated_withFirst of seven frieze types; has only translation symmetry, no rotations, reflections, or glide-reflections.
- p1m1 Frieze Patternassociated_withFourth frieze type; has horizontal mirror reflection symmetry parallel to translation axis but no rotation symmetry.
- Frieze Patternsassociated_withThe primary mathematical object of study; one-dimensional infinitely-repeating geometric patterns found in Islamic art.
- p112 Frieze Patternassociated_withSecond frieze type; has two-fold rotational symmetry but no reflections or glide-reflections.
- p1g1 Frieze Patternassociated_withSeventh and rarest frieze type; has glide-reflection symmetry along translation axis but no rotation or reflection symmetry.
- pm11 Frieze Patternassociated_withThird frieze type; has vertical mirror reflection symmetry but no rotation symmetry.
- pmg2 Frieze Patternassociated_withSixth frieze type; has two-fold rotational symmetry, vertical reflection symmetry, and glide-reflection symmetry.
- pmm2 Frieze Patternassociated_withFifth frieze type; has reflection symmetry in two directions and two-fold rotational symmetry.
Frameworks (2)
framework
- Seven frieze pattern groupsrelated_tosame_asClassification of one-dimensional periodic patterns into 7 symmetry groups using international notation pxyz
- Wallpaper Groupsassociated_withMathematical classification system for two-dimensional repeating patterns; mentioned as analogous to frieze groups.
Related by similarity (6)
cosine ≥ 0.65 · no typed edgeEntities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.
- Author's survey of Alhambra ornamentation yielded all seven types
- The seven categories (Objective only, Expect only, Compare only, and four combinations) structuring the experiment
- Extension to frieze patterns of the observed rarity in wallpaper groups
- A principle from physics that when symmetry is broken, a system acts to preserve as many of its symmetries as possible, preserving as much structure as possible.