Tile-Makers and Semi-Tile-Makers

Jin Akiyama
Research Institute of Educational Development,
Tokai University, Tokyo 151-8677,
Japan

Abstract
We mean by a development (Fig. 1) of a polyhedron a connected plane figure obtained by cutting the surface along any parts of its surface, not necessarily along its sides. So there are infinitely many developments for a polyhedron. A polyhedron V is said to be a tile-maker if every development of V is a tiler.

By a side-development (Fig. 2) of a polyhedron V, we mean a special kind of developments obtained by cutting the surface of V along sides of V only. A polyhedron V is said to be a semi-tile-maker if every side-development of V is a tiler.

We determine all tile-makers and show some examples of semi-tile-makers.

Fig.1

Fig.2