Animation of Some Truncated Polyhedrons

Takashi Soma¹ and Yasunari Watanabe²

¹Department of Mathematics and Computing Science, The University of the South Pacific, P.O. Box 1168, Suva, Fiji
E-mail: soma_t@manu.usp.ac.fj
²Department of Information Systems, Teikyo Heisei University, 289 Uruido, Ichihara, Chiba 290-0193, Japan
E-mail: watanabe@thu.ac.jp

(Received January 7, 2000; Accepted January 27, 2000)

Keywords: Animation, Mixing, n-Star, Polyhedron, Truncation

Abstract. A rhombic enneacontahedron consists of two kinds of equilateral rhombuses, fat and thin. There are thirty thin rhombuses whose normals are the same as those of a triacontahedron. This shows that the enneacontahedron is a polyhedron truncated by a triacontahedron and it can be transformed into a triacontahedron by increasing the depth of truncation. This change from an enneacontahedron to a triacontahedron is shown by animation using a 3D viewer called Geomview available from the Geometry Center of the University of Minnesota. The software called Qhull, also available from the Geometry Center, which finds a convex hull for given points is used to find the truncated polyhedron. Also shown are a rhombic dodecahedron truncated by a hexahedron with different depths of truncation, and 3D sections of the 4D test polytope with different sectioning positions for 3D Beenker pattern.