Artists
Theo Schaad
Artist
Physics Department, University of Washington
Seattle, Washington, USA
Statement
I make many of my polyhedra with heavy card stock in the style of Magnus Wenninger's polyhedron models, usually with each face cut out separately with tabs and glued together. This is clearly not pure origami that is folded from one sheet of paper. But when I searched the internet to find similar models to my tori that I will submit this year, I always found references to modular origami. And none of them had icosahedral modules. The Platonic icosahedron does not make a complete torus and may have discouraged origamists from using it.
Artworks
N-Fold Icosahedral Tori
33.0 x 33.0 x 8.0 cm
Heavy card stock
2025
N-Fold Icosahedral Tori are toroidal polyhedra with N-fold rotational symmetry. They are related to modular origami where each module is a polyhedron that is repeated N times to make a complete torus. The modules are icosahedra with 20 triangular faces; hence the modular part is icosahedral. I discovered that I could change one edge of a regular Platonic icosahedron and turn two equilateral triangles into isosceles triangles. The real challenge was to find the length of the altered edge to make a complete torus with exactly N modules. I constructed models from N=4 to N=14.