Geodesic
Isohedrally compatible tilings
Two of the 17 (plane) crystallographic groups, G and H, are isohedrally compatible if there exists a tile which admits separate tilings with respective automorphism groups G and H. The purpose of this article is to show that of the 136 possible pairs, 77 are definitely compatible, 44 are not and we conjecture the remaining 15 pairs are also not compatible.
Classification : 05B45 52C2052C22 
@article{VM_2002_4_4_a0,
     author = {Philip M. Maynard},
     title = {Isohedrally compatible tilings},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2002_4_4_a0/}
}
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Philip M. Maynard. Isohedrally compatible tilings. Visual Mathematics, Tome 4 (2002) no. 4. http://geodesic.mathdoc.fr/item/VM_2002_4_4_a0/