Institute of Technology, USA, 2 Georgia Institute of Technology, USA http://thomas.grasl.com/subgroups/ 1 economou@coa.gatech.edu A computational approach for the generation of all partial lattices of twodimensional shapes with an n-fold symmetry axis is presented and an application in formal analysis in architectural design is presented in the end. Keywords: Shape studies; generative design; group theory; graph theory; shape grammars; central buildings. Introduction Group theory has been extensively used in systematic studies in analysis and synthesis of form. This could hardly be otherwise as long as group theory provides the mathematical language for symmetry and symmetry has been one of the cornerstones of formal composition in architectural design and in the arts in general (see for example, Weyl, 1952; Shubnikov and Koptsik, 1974; March and Steadman, 1974).
| Authors | Athanassios Economou and Thomas Grasl |
|---|---|
| Year | 2007 |
| Venue | Proceedings of the 25th International Conference on Education and Research in Computer Aided Architectural Design in Europe (eCAADe) |
| DOI | 10.52842/CONF.ECAADE.2007.947 |
| Source Database | Seed (CumInCAD) |
| Bridge-to-GNN | Category Seed |
| GNN Architecture | Not yet extracted from PDF |
| Graph Encoding | Not yet extracted from PDF |
| AEC Task | Not yet extracted from PDF |
| Cohort | Early Infrastructure (2020–2021) |
| Primary Metric | R² (heuristic — verify) |
|---|
| GNN architectures detected | Knowledge Graph Embedding (TransE/RotatE/DistMult) |
|---|---|
| Quality (heuristic, 6-flag) | 0/6 · rigor: Low Code/Data: —Benchmark: —Baseline: —CV/Split: —Ablation: —Reproducible: — |
Part of the GML/GNN in AEC Systematic Review (PRISMA 2020) — 112 papers, 2020–2026