glide-reflections in frieze patterns may also be rare

Extension to frieze patterns of the observed rarity in wallpaper groups

Source paper

extracted_from

(2007) · Bodner, B. Lynn

paper

finding

claim

Glide-reflections appear to be a less-favored symmetry for Islamic planar mosaic tilings.
extends
Bodner's interpretive finding based on comparative analysis; supported by Abas and Salman's statistical distribution data.

cosine ≥ 0.65 · no typed edge

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

Determining whether or not a pattern has glide-reflection symmetry can be challengingclaim0.825
Author's methodological note about subtlety of glide-reflections
Glide-reflections appear to be less-favored symmetries in Islamic geometric patterns compared to other isometries.claim0.822
Glide-Reflection Symmetryconcept0.797
One of four key isometries; combination of reflection and translation parallel to the mirror line.
Frieze Patternsconcept0.746
The primary mathematical object of study; one-dimensional infinitely-repeating geometric patterns found in Islamic art.
The p1g1 frieze class appears very rarely in Islamic mosaic tilings at the Alhambra and was entirely absent at Real Alcázar.finding0.738
p1g1 Frieze Patternconcept0.734
Seventh and rarest frieze type; has glide-reflection symmetry along translation axis but no rotation or reflection symmetry.
Symmetries and frieze groups mathematically capture design pattern properties.claim0.723
p1m1 Frieze Patternconcept0.723
Fourth frieze type; has horizontal mirror reflection symmetry parallel to translation axis but no rotation symmetry.