Fetching the paper…
Reading the bibliography…
We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk.
Math. Zeitschr. 91
Wilkie, H.C.: On non-Euclidean crystallographic groups · 1966
Earlier work this paper cites.
Canadian Journal of Mathematics 19
Macbeath, A.M.: The classification of non-euclidean plane crystallographic groups · 1967
Earlier work this paper cites.
Math. Zeitschr. 125
Hoare, A.H.M., Karrass, A., Solitar, D.: Subgroups of Infinite Index in Fuchsian Groups · 1972
Earlier work this paper cites.
Communications on Pure and Applied Mathematics XXVI
Hoare, A.H.M., Karrass, A., Solitar, D.: Subgroups of NEC Groups · 1973
Earlier work this paper cites.
Princeton lecture notes (1980)
Thurston, W.: Geometry and Topology of Three-Manifolds · 1980
Earlier work this paper cites.
Wollny, W.: Dualität von cayley-diagramm und fundamentalbereichsparkett bei den diskreten 1-dimensionalen bewegungsgruppen · 1981
Earlier work this paper cites.
Advances in Mathematics 63
Dress, A.W.: Presentations of discrete groups, acting on simply connected manifolds, in terms of parametrized systems of coxeter matrices-a systematic approach · 1987
Earlier work this paper cites.
Geometriae Dedicata 24
Dress, A.W.M., Huson, D.: On tilings of the plane · 1987
Earlier work this paper cites.
Freeman and Co. (1987)
Grünbaum, B., Shephard, G.C.: Tilings and patterns · 1987
Earlier work this paper cites.
Acta Crystallogr A 45
Sadoc, J., Charvolin, J.: Infinite periodic minimal surfaces and their crystallography in the hyperbolic plane · 1989
Earlier work this paper cites.
Archiv der Mathematik 54
Lučić, Z., Molnär, E.: Combinatorial classification of fundamental domains of finite area for planar discontinuous isometry groups · 1990
Earlier work this paper cites.
Geometriae Dedicata 40
Lučić, Z., Molnár, E.: Fundamental domains for planar discontinuous groups and uniform tilings · 1991
Cited alongside, same era.
Geometriae Dedicata 47
Huson, D.H.: The generation and classification of tile-k-transitive tilings of the euclidean plane, the sphere and the hyperbolic plane · 1993
Cited alongside, same era.
Contributions to Algebra and Geometry 34
Huson, D.H.: Tile-transitive partial tilings of the plane · 1993
Cited alongside, same era.
Elsevier Science (1996)
Hyde, S.T., Landh, T., Lidin, S., Ninham, B., Larsson, K., Andersson, S.: The Language of Shape · 1996
Cited alongside, same era.
European Physical Journal B 16
Hyde, S.T., Oguey, C.: From 2D hyperbolic forests to 3D Euclidean entangled thickets · 2000
Cited alongside, same era.
Structural Chemistry 13
Conway, J.H., Huson, D.H.: The orbifold notation for two-dimensional groups · 2002
Cited alongside, same era.
CRC Press (2008)
Conway, J.H., Burgiel, H., Goodman-Strauss, C.: The Symmetry of Things · 2008
Later among the works it cites.
American Mathematical Society (2008)
Friedrich, T., Agricola, I.: Elementary Geometry · 2008
Later among the works it cites.
Biomaterials 32
Kapfer, S.C., Hyde, S.T., Mecke, K., Arns, C.H., Schröder-Turk, G.E.: Minimal surface scaffold designs for tissue engineering · 2011
Later among the works it cites.
Acta Crystallographica Section A 69
Evans, M.E., Robins, V., Hyde, S.T.: Periodic entanglement i: networks from hyperbolic reticulations · 2013
Later among the works it cites.
Acta Crystallographica Section A 69
Evans, M.E., Robins, V., Hyde, S.T.: Periodic entanglement ii: weavings from hyperbolic line patterns · 2013
Later among the works it cites.
Proceedings of the National Academy of Sciences of the United States of America 111
Kirkensgaard, J.J.K., Evans, M.E., de Campo, L., Hyde, S.T.: Hierarchical self-assembly of a striped gyroid formed by threaded chiral mesoscale networks · 2014
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Nature 419
Sharon, E., Roman, B., Marder, M., Shin, G.S., Swinney, H.L.: Buckling cascades in free sheets · 2002
Cited alongside, same era.
Springer Monographs in Mathematics. Springer Berlin Heidelberg (2002)
Stilwell, J., Serre, J.: Trees · 2002
Cited alongside, same era.
Theoretical Computer Science 303
Delgado-Friedrichs, O.: Data structures and algorithms for tilings I · 2003
Cited alongside, same era.
European Physical Journal B 48
Robins, V., Ramsden, S.J., Hyde, S.T.: A note on the two symmetry-preserving covering maps of the gyroid minimal surface · 2005
Cited alongside, same era.
Graduate Texts in Mathematics. Springer New York (2006)
Ratcliffe, J.: Foundations of Hyperbolic Manifolds · 2006
Cited alongside, same era.
Later among the works it cites.
Acta Crystallographica Section A 71
Evans, M.E., Hyde, S.T.: Periodic entanglement III: tangled degree-3 finite and layer net intergrowths from rare forests · 2015
Later among the works it cites.
Interface Focus 7
de Campo, L., Castle, T., Hyde, S.T.: Optimal packings of three-arm star polyphiles: from tricontinuous to quasi-uniformly striped bicontinuous forms · 2016
Later among the works it cites.
In: M.D.E. Conder, A. Deza, A.I. Weiss (eds.) Discrete Geometry and Symmetry, pp. 257–278. Springer International Publishing, Cham (2018)
Lučić, Z., Molnár, E., Vasiljević, N.: An algorithm for classification of fundamental polygons for a plane discontinuous group · 2018
Later among the works it cites.
Proceedings of the National Academy of Sciences 115
Pedersen, M.C., Hyde, S.T.: Polyhedra and packings from hyperbolic honeycombs · 2018
Later among the works it cites.
http://epinet.anu.edu.au/
Ramsden, S., Robins, V., Hyde, S.: Euclidean patterns in non-euclidean tilings · 2019
Closest in time.