Forma, Vol. 15 (No. 1), pp. 67-73, 2000
Original Paper

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
2Department of Information Systems, Teikyo Heisei University, 289 Uruido, Ichihara, Chiba 290-0193, Japan

(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.

[Full text] (PDF 360 KB)