Spidron Domain The Expanding Spidron Universe

Year: 2006 Authors: Daniel Erdély; Marc Pelletier

Core claim

Spidron constructions extend into new tilings, solids, and network assemblies with potential for puzzles and sculpture.

Topics

Spidron geometry, tilings and reliefs, polyhedra, non-periodic networks

Domains

geometry, polyhedra, tiling theory, discrete mathematics, sculpture, mathematical art, relief design, puzzle design

Methods

geometric construction, tiling exploration, polyhedral dissection, modular assembly

Media

paper models, 2.5-dimensional reliefs, rhombohedra, images

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

Daniel Erdély & Marc Pelletier H-1015 Budapest, Battyany str. 31. I./12. email: edan@spidron.hu www.spidron.hu

Abstract

A number of new discoveries have been made since the last Bridges conference in the area of Spidron research. Shown here are samples of what will be presented in London.

1. Two Dimensions & 2.5 Dimensional Reliefs

Spidron versions of the Penrose-Richert tiles have been discovered, as well as a negative space partner to the classic spidron diamond. Two more reliefs based on semi-regular tilings were also discovered, one based on the tiling of squares and octagons and the other based on tiling of squares, hexagons and dodecagons.

Figures 1 and 2: Two new semiregular Spidron reliefs

2. The Splatonic Solids and the Archimedians

In addition to the already known Tetra-Spidro ball and the Octa-Spidro ball, there are three other solids corresponding to the Platonics. Also there are 10 other semiregular Spidron solids. A number of linkage puzzles have been discovered from these shapes.

Figures 3 and 4: The Splatonics (left), and two Archimedians and eight Quasi-Archemedians (right)

3. Platonic Disections and Prism Towers

The Platonic solids can be dissected along skew polygons and we’ve found a family of prisms and towers.

Figures 5 and 6: Platonic dissections (left) and Prism towers (right)

4. Non-Periodic Spidron Networks

The A6 and O6 rhombohedra can be used as building blocks for non-periodic arrangements of Spridron nests, with great potential for sculpture.

Figure 7: The A6 and O6 building blocks

Special thanks to Amina Allen, Rinus Roelofs, and Walt van Ballegooijen.

For more about Spidrons, refer to D. Erdély, Some Surprising New Properties of Spidrons, Renaissance Bridges Proceedings (2005) p. 179-186