A229757 Numbers n such that no convex hexagon exists that can be dissected into n congruent equilateral triangles.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 15, 17, 20, 21, 23, 29, 36, 39, 41, 44, 84

Offset: 1

Author

Suggested by Eike Hertel, Hugo Pfoertner, Sep 28 2013

Keywords

• nonn
• fini
• full

Comments

Numbers not expressible as k = 2*(a*c + b*c + b*d) - (a-d)^2 with a,b,c,d >= 1, a < c+d, d < a+b.

See the Hertel paper for the finiteness proof.

Links

• Eike Hertel, Reguläre Dreieckspflasterungen konvexer Polygone, Jenaer Schriften zur Mathematik und Informatik, Math/Inf/01/13, 2013 (preprint).
• Eike Hertel, Christian Richter, Tiling Convex Polygons with Congruent Equilateral Triangles, Discrete Comput Geom (2014) 51:753-759.
• Kival Ngaokrajang, Illustration of initial terms

Crossrefs

Cf. A229461 (Pentagon exception numbers).