Wednesday, June 22, 2016

[obwwlxut] Gluing polyhedra

Consider gluing matching faces of polyhedra, building structures.  For example, regular dodecahedra will not tesselate space, but I suspect one can build interesting helices (spirals).  Boerdijk-Coxeter helix.

Limit to polyhedra with faces with regular polygons of unit side length to keep things simple.  Though star faces and star polyhedra could be included.

Hinges if relaxing to join only at an edge. Joints for joining only at a vertex. Restrictions of faces to regular, and edges to be unit length, can correspondingly be relaxed.

Previously similar in 2D.

Easiest to do it in virtual reality.  In 2D or 3D we seek user interface tools which provide nice feedback when a polygon or polyhedron clicks into place correctly next to another one.

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