Emotional responses to school façade opening geometries associated with the golden ratio among high school girls in Babol, Iran

Abstract School façades are often the first architectural element students encounter, yet students’ aesthetic and emotional preferences are rarely incorporated into façade design decisions. This study examines how the geometry of façade openings relates to high-school students’ emotional responses, with a particular focus on forms associated with the golden ratio and Iranian proportional systems. We hypothesised that hexagonal openings, rooted in the Iranian proportional tradition, would be associated with more positive emotional appraisals than openings based on the conventional golden-ratio rectangle, the golden triangle, or strongly elongated rectangles. A semantic differential questionnaire using a seven-point Likert scale was administered to third-grade female high-school students in Babol, Iran ( n = 327), across three study tracks (mathematics, experimental sciences, and humanities) and two school types (public and private). Participants evaluated five façade alternatives that differed only in opening geometry. Because all participants rated all five alternatives, the data were analysed as repeated measures. Shapiro–Wilk tests indicated non-normal distributions for all opening-by-attribute combinations (all p < .001); therefore, Friedman tests were used, followed by Holm-adjusted Wilcoxon signed-rank comparisons. Kendall’s W and matched-pairs rank-biserial correlations were reported as effect sizes. The overall 21-attribute rating differed significantly among opening types, χ²(4, N = 327) = 104.29, Holm-adjusted p < .001, Kendall’s W = 0.080. The hexagonal opening had the highest overall mean (M = 4.421) and was rated significantly higher than each of the other four openings in Holm-adjusted pairwise comparisons. It also had the highest mean on 18 of 21 individual attributes. Attribute-level effect sizes were mostly small (Kendall’s W = 0.018–0.137). The findings suggest that hexagonal openings - historically connected to Iranian proportional geometry - are associated with more positive self-reported emotional responses to high-school façade images. For educators and school designers, incorporating user-centred evidence such as this into early façade design decisions may help create schools that students experience as more welcoming, though the present study measures reported emotional and aesthetic preferences rather than learning outcomes or well-being directly.