Geodesic
Non-fundamental 2-isohedral tilings of the sphere
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2008), pp. 35-45.

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The investigation of 2-isohedral tilings of the 2-dimensional sphere is continued. In previous works all the fundamental 2-isohedral tilings of the sphere have been enumerated. Here non-fundamental 2-isohedral tilings of the sphere are obtained from the fundamental ones using the method of gluing disks. For all the 7 countable series of isometry groups of the sphere the classification of normal non-fundamental tilings is given in a table of pictures. For non-normal tilings only numerical results are given. For the 7 separate isometry groups of the sphere numerical results are also shown. 
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Elizaveta Zamorzaeva. Non-fundamental 2-isohedral tilings of the sphere. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2008), pp. 35-45. https://geodesic-test.mathdoc.fr/item/BASM_2008_2_a3/

[1] Grünbaum B., Shephard G.C., “Spherical tilings with transitivity properties”, The Geometric Vein. The Coxeter Festschrift, Springer-Verlag, New York–Heidelberg–Berlin, 1981, 65–98 | MR

[2] Grünbaum B., Shephard G.C., “The 2-homeotoxal tilings of the plane and 2-sphere”, J. Combin. Theory, Ser. B, 34:3 (1983), 113–150 | DOI | MR | Zbl

[3] Zamorzaeva E.A., “On sorts of two-dimensional multiregular tilings”, Izv. Akad. Nauk Respub. Moldova. Matematika, 1992, no. 1, 59–66 (in Russian) | MR | Zbl

[4] Zamorzaeva E.A., “Classification of 2-isohedral tilings of the sphere”, Bul. Acad. Şt. Rep. Moldova. Matematica, 1997, no. 3, 74–85 (in Russian) | MR | Zbl

[5] Zamorzaeva E., “Enumeration of 2-isohedral tilings on the sphere”, Visual Mathematics (electronic journal), 6:1 (2004) | Zbl

[6] Huson D.H., “The generation and classification of tile-$k$-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane”, Geom. Dedicata, 47 (1993), 269–296 | DOI | MR | Zbl

[7] Delgado O., Huson D., Zamorzaeva E., “The classification of 2-isohedral tilings of the plane”, Geom. Dedicata, 43 (1992), 43–117 | MR | Zbl

[8] Balke L., Huson D.H., “Two-dimensional groups, orbifolds and tilings”, Geom. Dedicata, 60 (1996), 89–106 | DOI | MR | Zbl

[9] Proc. Steklov Inst. Math., 4 (1980), 111–141 | MR | Zbl