Geometry research

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Kabai, S., Bérczi, Sz., & Szilassi, L. (2012). Clusters Produced by Placing Rhombic Triacontahedra at the Vertices of Polyhedra. The Mathematica Journal, 14. https://doi.org/10.3888/tmj.14-14Publisher / online source

This article explores geometric clusters built from thirty-faced solids with rhombic faces. Placing these solids at the vertices of other polyhedra reveals different spatial arrangements and symmetries. Source

Kabai, S., & Bérczi, Sz. (2003). Crystallography of a space station, Part I: How to build stellated rhombic tricontahedral structures from golden rhombohedra by folding and docking. Symmetry: Culture and Science, 11(1–4), 361–378.

Bérczi, Sz. (2003). From the Periodic System of Platonic and Archimedean Solids and Tessellations to the 4D Regular Polyhedra and Tessellations (with Extensions to Some 5D Polytopes). Symmetry: Culture and Science, 11(1-4), 125–137.

Berczi, Sz., Kabai, S., & Miura, Y. (2003). Models of Spongy Material Structures with Quasicrystalline Microstructure; Their Construction from Golden Rhonbohedral Units - Their Representation by Impact Materials with Fivefold Symmetry. International Symposium on Impact Events in Japan, Southeast Asia and Pacific Rim. Yamaguchi, Japan, November 21-25, 2003.

Bérczi, Sz. (1993). Double Layered Equation of Motion: Platonic and Archimedean Cellular Automata in the Solution of the Indirect Von Neumann Problem on Sphere for Transformations of regular Tessellations. Acta Mineralogica et Petrographica, 39, 96–117.

Bérczi, Sz. (1991). Platonic-Archimedean Spherical Cellular Automata in the Solution of the Indirect Von-Neumann Problem on Sphere for Transformations of Regular Tessellations. In B. Lukács, Sz. Bérczi, I. Molnár, & Gy. Paál (Eds.), Symmetry and topology in evolution (MTA-KFKI-1991-32/C; pp. 111–116). MTA Központi Fizikai Kutatóintézet.

Bérczi, Sz. (1980). The Periodic System of Platonic and Archimedean Solids and Tessellations. Acta Geologica Acad. Sci. Hung., 23(1-4), 184–200.

Bérczi, Sz., & Nagy, D. (1979). Lockwood, E. H. and Macmillan, R. H.: Geometric Symmetry. (Book review). Acta Scientiarum Mathematicarum, 41(3-4).

Bérczi, Sz. (1978). The Periodic System of Platonic and Archimedean Solids and Tessellations [Presentation]. Cyclicity: Theory and Practice Conference, Budapest, 1978, November.

Bérczi, Sz. (2016). Structural hierarchy. Symmetry: Culture and Science, 27(1), 11–22.

Bérczi, Sz. (2005). Changes in Symmetry Caused by Cellular Automata Transformations of Closed Double Fibers and Cellular Tubes with Möbius Band, Torus, Tube Knot, and Klien Bottle Topologies. In P. Weibel (Ed.), Beyond Art: A Third Culture: A Comparative Study in Cultures, Art and Science in 20th Century Austria and Hungary (pp. 616). 179-181. Springer.

Bense, L., Bérczi, Sz., Kabai, S., Eklund, G., Jorulf, H., & von Heijne, A. (2003). Symmetry, Structure, Hierarchy and Topology in a Bronchial Tree Structural Model of the Lung. In Symmetry Festival, Poster session (pp. N/A).

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Bérczi, Sz., & Lukács, B. (1996). The Water-Ammonia Symmetry of Amino Acids: Constraints on Paleoatmospheres. Acta Climatologica, 30, 5–30.

Kubovics, I., Bérczi, Sz., Józsa, S., Szakmány, Gy., & Török, K. (1994). Description of Petrological Processes with Cellular Automatic Form: a Cosmic, a Volcanic and a Metamorphic Sequence. In B. Lukács, I. Kubovics, L. Stegena, & Sz. Bérczi (Eds.), Evolution of extraterrestrial materials and structures (MTA-KFKI-1994-22/C; pp. 104–116). MTA Központi Fizikai Kutatóintézet.

Bérczi, Sz. (1993). Symmetry and Topology in Cellular Automatic Transformations, The Solution of the Indirect Von Neumann Problem for the Transfiguratuions of Cylindrical Cell-Mosaic systems of Fibonacci Plants. Abstracta Botanica, 17, 225–239.

Bérczi, Sz. (1993). Symmetry Changes by Cellular Automata in Transformations of Closed Double-Threads and Cellular Tubes with Möbius-Band, Torus, Tube-Knot and Klein-Bottle Topologies. Symmetry: Culture and Science, 4(1), 49–68.Full text (ResearchGate)

Bérczi, Sz. (1992). The Indirect Von-Neumann Problem: Deciphering of the Local Transformations from the Global Ones of the Systems Structurally Determined by the Both Hierarchy Levels of Their Symmetry. In B. Lukács, Sz. Bérczi, E. Lábos, & I. Molnár (Eds.), Mutual dynamics of organizational levels in evolution (MTA-KFKI-1992-32/C; pp. 40–49). MTA Központi Fizikai Kutatóintézet.

Bérczi, Sz. (1991). Cellular Automata models of plant surface lattices [Presentation]. Lecture on I3rd Congress of the European Society of Evolutionary Biology. Debrecen, 1991, September.

Bérczi, Sz. (1991). Platonic-Archimedean Cellular Automata. (pp. 111-116). In B. Lukács, Sz. Bérczi, I. Molnár, & Gy. Paál (Eds.), Symmetry and topology in evolution (MTA-KFKI-1991-32/C; pp. 1991–32). MTA Központi Fizikai Kutatóintézet.

Bérczi, Sz. (1991). Symmetry by Cellular Automata. Lect. on Intuitive Geometry Conference. Szeged, 1991 September.

Bérczi, Sz. (1991). Symmetry by Cellular Automata [Presentation]. Lecture on Intuitive Geometry Conference. Szeged, 1991, September.

Bérczi, Sz. (1991). Symmetry Changes by Cellular Automata in Transformations of Closed Double-Threads and Cellular Tubes with Möbius-Band, Torus, Tube-Knot and Klein-Bottle Topologies. In B. Lukács, Sz. Bérczi, I. Molnár, & Gy. Paál (Eds.), Symmetry and topology in evolution (MTA-KFKI-1991-32/C; pp. 29–41). MTA Központi Fizikai Kutatóintézet.

Bérczi, Sz. (1990). Symmetry Constraints in Development and Evolution of Fibonacci Plants. [. In J. Maynard-Smith & G. Vida (Eds.), Organizational constraints on the dynamics of evolution (pp. 79–88). Manchester University Press.

Bérczi, Sz. (1987). Symmetry Constraints in Development and Evolution of Fibonacci-Plants. Symposium on Organizational Constraints on the Dynamics of Evolution, Budapest 1987. jún. 29. - júl. 3.

Bérczi, Sz. (1985). Symmetries in the Plant Surface Lattice Systems: Development of Fibonacci Numbered Structure in a Cellular Automaton Model [Presentation]. Lect. on Intuitive Geometry Conference. 1985. May 15. Balatonszéplak.