Peter Hilgers
I am a retired engineer, computer hobbyist, naive artist and have always been fascinated by geometry. Current computers and sophisticated programs make it possible to create, study and visualise complex structures. For me this is a constant source of challenges and delight.
The topic of this artwork is a playfully treated feature of
non-periodic tilings called growth form. Growth forms are a kind
of neighbourhood relation for 2D or 3D tilings: Let a patch P of a
tiling be a finite set of tiles. Under recently found general
conditions [1] the nth-generation "immediate neighbours" of P,
scaled by 1/n, form a defined polygon or polyhedron in the
limit.
Here the tiling is derived from 30 vectors related to an
octahedron 5 compound and the growth form is a convex polyhedron
with icosahedral symmetry, 590 vertices, 1260 edges and 672
faces.
[1] Demski, D., Hilgers, P. & Shutov, A.: Grow forms of grid
tilings, Acta Crystallographica, Volume A78, Part 4, 1 July 2022,
https://doi.org/10.1107/S2053273322003485