Modeling of Kepler-Poinsot Solid Using Isomorphic Polyhedral Graph

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.

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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.