Yoshiaki Araki

Japan Tessellation Design Association

In 1995, Marjorie Rice discovered an interesting tiling by using convex pentagons. The authors discovered novel properties of the tilings of convex pentagon which Rice used in the discovery. As a result, many new convex pentagon tilings (tessellations) were found. The convex pentagon tilings are related to tilings by heptiamonds.

In the previous manuscript, new tilings (tessellations) were presented using convex pentagonal tiles belonging to Type 1 and Type 5. The convex pentagon tilings are related to heptiamond tilings. Later, the authors found Johannes Hindriks' site that summarized the research results of heptiamond tilings (tessellations). In this manuscript, the resul...

In this paper, we investigate the common unfolding between regular tetrahedra and Johnson-Zalgaller solids. More precisely, we investigate the sets of all edge developments of Johnson-Zalgaller solids that fold into regular tetrahedra. We show that, among 92 Johnson-Zalgaller solids, only J17 (gyroelongated square dipyramid) and J84 (snub disphenoi...

[PROBLEM TO BE SOLVED] To reduce a server load when synchronizing data between a client and a server. [SOLUTION] A client 10 sends a synchronization request 41 containing an anchor point to a server 20. The server 20 sends synchronization information 42 to the client 10, which synchronization information including change profile information on data...

Let $\Gamma$ be a 3-dimensional Kleinian punctured torus group with ccidental parabolic transformations. The deformation space of $\Gamma$ in the group of M\"{o}bius transformations on the 2-sphere is well-known as the Maskit slice of punctured torus groups. In this paper, we study deformations $\Gamma'$ of $\Gamma$ in the group of M\"{o}bius trans...

We introduce new fascinating fractal shapes which are natively embedded in the three dimensional space. These are quasispheres, that is, the limit sets of three dimensional quasifuchsian groups. There were only few examples of three dimensional quasifuchsian groups and there was no visualization of the limit sets of them. We construct a new family...

In this paper, we introduce the design and implementation of VSPLUS, a high-level multi-user extension library to enable people to simultaneously manipulate interactive VRML worlds over networks. The key consideration of the VSPLUS design is the ease of creations of multi-user worlds from single-user standard VRML worlds without extensive programmi...

This paper reports experiments of materializing recent new discovered mathematical surfaces, 3D quasi-Fuchsian fractals. Three different models in glass, plastic, and metal are created to realize rich mathematical properties including self-similarity, 3-embeddable, simply-connected, and complicated surface consisting of infinite number of cusps. Di...