Challenge

Build by Face Adjacency

Photo of a 4-person yellow domed camping tent structure following face adjacency rules
A 4-person tent domed tent with pentagonal and triangular faces following face adjacency rules. Via Narukawa Lab & Goldwin Public Relations

Build shapes where the edges of triangular faces can only touch square faces and vice versa.

  • What happens when triangles can only touch pentagons, or only touch hexagons?
  • What about polyhedra and tessellations with three different shapes? What face adjacency rules can be applied?
  • How many polyhedra and 2D tessellations satisfy these conditions?
  • What other face adjacency rules create interesting shapes? What happens if you combine rules, add conditionals, and/or change rules mid-build?
  • How does face adjacency relate to edge adjacency and vertex valency in graph theory?

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