Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
Visualization of Conway Polyhedron Notation

Authors: Hidetoshi Nonaka

Abstract:

This paper presents an interactive modeling system of polyhedra using the isomorphic graphs. Especially, Conway polyhedron notation is implemented. The notation can be observed as interactive animation.

Keywords: Conway polyhedron notation, Polyhedral graph, Visualization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082955

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1973

References:


[1] G. W. Hart, "Conway Notation for Polyhedra", URL: http://www.gergehart.co/virtual-polyhedra/conway_notation.html.
[2] E. W. Weisstein, "Conway Polyhedron Notation", MathWorld.
[3] H. S. M. Coxeter, "Regular Polytopes", Dover Publications, 1973.
[4] P. Martin, and D. Martin, "PolyFormes: Software for the declarative modelling of polyhedra", The Visual Computer, 15 (2), pp. 55-76, 1999.
[5] G. W. Hart, and H. Picciotto, "Zome Geometry: Hands on Learning With Zome Models", Key Curriculum Pr., 2001.
[6] A. Holden, "Shapes, Space, and Symmetry", Columbia University Press, 1971
[7] T. Nishizeki and N. Chiba, "Planar Graphs - Theory and Algorithms", Dover Publications, 1988.
[8] T. Tyler, "Springie: A tensegrity simulator using Java, VRML and POV Ray", http://springie.com/.
[9] K. Inoue, K. Shimada, and K. Chilaka, "Solid Model Reconstruction of Wireframe CAD Models Based on Topological Embeddings of Planar Graphs", Journal of Mechanical Design, 125, pp. 434-442, 2003.
[10] B. Gr├╝nbaum, "Graphs of polyhedra; polyhedra as graphs", Discrete Mathematics, 307, pp. 445-463, 2007.
[11] H. Nonaka, "Detection of Faces in Wire-Frame Polyhedra", Proceedings of International Conference on Computer Graphics Theory and Applications, pp. 134-137, Jan. 2008.
[12] H. Nonaka, "Interactive Modeling of Uniform Polyhedra by Means of Graph Drawing", Proceedings of International Conference on Information Technology and Applications, 5, 822-827, 2008
[13] H. Nonaka, "Operation-Based Notation for Archimedean Graph", Proceedings of World Multi-Conference on Systemics, Cybernetics and Informatics, 12, 2008.
[14] H. Nonaka, "Modeling of Kepler-Poinsot Solid Using Isomorphic Polyhedral Graph", International Journal of Computer Science, 3 (1) 64-67, 2008, http://www.waset.org/ijcs/former.html