Tetrad (geometry puzzle) explained
In
geometry, a
tetrad is a set of four
simply connected disjoint planar regions in the plane, each pair sharing a finite portion of common boundary. It was named by Michael R. W. Buckley in 1975 in the
Journal of Recreational Mathematics. A further question was proposed that became a puzzle, whether the 4 regions could be congruent, with or without
holes, other enclosed regions.
[1] Fewest sides and vertices
The solutions with four congruent tiles include some with five sides.[2] However, their placement surrounds an uncovered hole in the plane. Among solutions without holes, the ones with the fewest possible sides are given by a hexagon identified by Scott Kim as a student at Stanford University.[1] It is not known whether five-sided solutions without holes are possible.[2]
Kim's solution has 16 vertices, while some of the pentagon solutions have as few as 11 vertices. It is not known whether fewer vertices are possible.[2]
Congruent polyform solutions
Gardner offered a number of polyform (polyomino, polyiamond, and polyhex) solutions, with no holes.[1]
External links
Notes and References
- Martin Gardner, Penrose Tiles to Trapdoor ciphers, 1989, p.121-123 https://books.google.com/books?id=P1AFEAAAQBAJ&dq=Michael+R.+W.+Buckley+tetrad&pg=PA121
- https://www.trump.de/tetrads/ Further Questions about Tetrads
