Modeling of Kepler-Poinsot Solid Using Isomorphic Polyhedral Graph

Authors: Hidetoshi Nonaka

Abstract:

This paper presents an interactive modeling system of uniform polyhedra using the isomorphic graphs. Especially, Kepler-Poinsot solids are formed by modifications of dodecahedron and icosahedron.

Keywords: Kepler-Poinsot solid, Shape modeling, Polyhedralgraph, Graph drawing.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077845

References:

[1] H. S. M. Coxeter, "Regular Polytopes", Dover Publications, 1973
[2] P. Martin, and D. Martin, "PolyFormes: Software for the declarative modelling of polyhedra", The Visual Computer, 15 (2), pp. 55-76, 1999
[3] G. W. Hart, and H. Picciotto, "Zome Geometry: Hands on Learning With Zome Models", Key Curriculum Pr., 2001.
[4] G. W. Hart, "Virtual Polyhedra --- The Encyclopedia of Polyhedra", http://www.georgehart.com/virtual-polyhedra/vp.html
[5] G. W. Hart, "Conway Notation for Polyhedra", available at the URL: http://www.georgehart.co/virtual-polyhedra/conway_notation.html"
[6] A. Holden, "Shapes, Space, and Symmetry", Columbia University Press, 1971
[7] H. S. M. Coxeter, et al., "Fifty-Nine Icosahedra", Tarquin Publications, Norfolk, England, 1999
[8] J. Skilling, "The Complete Set of Uniform Polyhedra", Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical Science, 278, pp. 111-135, 1975
[9] T. A. Möller, and E. Haines, "Real-time Rendering",A K Peters, Ldt., 2002
[10] J. X. Chen, Y. Yang, and X. Wang, "Phisics-Based Modeling and Real-Time Simulation", Computing in Science & Engineering, 3, pp. 98-102, 2001.
[11] T. Tyler, "Springie: A tensegrity simulator using Java, VRML and POV Ray", http://springie.com/
[12] 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.
[13] H. Nonaka, "Detection of Faces in Wire-Frame Polyhedra", Proceedings of International Conference on Computer Graphics Theory and Applications, pp. 134-137, Jan. 2008.
[14] B. Gr├╝nbaum, "Graphs of polyhedra; polyhedra as graphs", Discrete Mathematics, 307, pp. 445-463, 2007.