Plane tilings
Posted: Fri Aug 21, 2015 9:32 am
Would it be possible for Stella to explore plane tilings as well as polyhedra?
There seem to be two approaches to tiling:
Symmetries (e.g. kaleidoscopes) in the plane can generate tilings, much as spherical ones generate polyhedra. There are even some "dense" or overlapping tilings analogous to star polyhedra. Could Stella be adapted to do this?
Given a particular tile, copies can be packed to fill the plane. Commonly, corners of some tiles are allowed to lie along the edge of another. This has no real analogy with polyhedra and I doubt that Stella could be merely adapted.
Aperiodic tilings seem to sit halfway between. The observation that say the Penrose tiling represents a slice or section through a higher-dimensional periodic spacefilling suggests that an extension to higher dimensions might be useful too.
There seem to be two approaches to tiling:
Symmetries (e.g. kaleidoscopes) in the plane can generate tilings, much as spherical ones generate polyhedra. There are even some "dense" or overlapping tilings analogous to star polyhedra. Could Stella be adapted to do this?
Given a particular tile, copies can be packed to fill the plane. Commonly, corners of some tiles are allowed to lie along the edge of another. This has no real analogy with polyhedra and I doubt that Stella could be merely adapted.
Aperiodic tilings seem to sit halfway between. The observation that say the Penrose tiling represents a slice or section through a higher-dimensional periodic spacefilling suggests that an extension to higher dimensions might be useful too.