Heesch's Problem

How many times can a shape be completely surrounded by copies of itself without being able to Tile the entireplane, i.e., what is the maximum (finite) Heesch Number?

References

Eppstein, D. ``Heesch's Problem.'' http://www.ics.uci.edu/~eppstein/junkyard/heesch/.

• Elongated Orthobicupola
• Elongated Orthobirotunda
• Elongated Orthocupolarotunda
• Elongated Pentagonal Cupola
• Elongated Pentagonal Dipyramid
• Elongated Pentagonal Gyrobicupola
• Elongated Pentagonal Gyrobirotunda
• Elongated Pentagonal Gyrocupolarotunda
• Elongated Pentagonal Orthobicupola
• Elongated Pentagonal Orthobirotunda
• Elongated Pentagonal Orthocupolarotunda
• Elongated Pentagonal Pyramid
• Elongated Pentagonal Rotunda
• Elongated Pyramid
• Elongated Rotunda
• Elongated Square Cupola
• Elongated Square Dipyramid
• Elongated Square Gyrobicupola
• Elongated Square Pyramid
• Elongated Triangular Cupola
• Elongated Triangular Dipyramid
• Elongated Triangular Gyrobicupola
• Elongated Triangular Orthobicupola
• Elongated Triangular Pyramid
• Elsasser Function