Sphairahedra and Three-Dimensional Fractals
Kento Nakamura and Kazushi Ahara

Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture
Pages 171–178
Regular Papers

Abstract

In 2003, Kazushi Ahara and Yoshiaki Araki introduced sphairahedra, which are analogous to polyhedra but with spherical faces, in order to invent a new kind of fractal shape. Using inversions in faces of a sphairahedron, we can construct a tiling pattern of sphairahedra. In many cases, the boundary of the tiling converges to a three-dimensional fractal shape. Despite its interesting idea and impressive shape, there are few publications and computer graphics images. In this paper, we show variations of sphairahedra and their tiling patterns that were never visualized.

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