B. Grunbaum and G. C. Shephard, Spherical tilings with transitivity properties, in The Geometric Vein (ed. C. Davis, B. Grunbaum, F. A. Sherk), 65--98, Springer-Verlag, New York, 1981. Home/Search Document Not in Database Summary Related Articles Check |
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Classification of Tilings of the 2-Dimensional Sphere By.. - Ueno, Agaoka (Correct)
....is a multiple of 4, except for G 4n 2 (n 1) In the case F 0 (mod 4) such tilings are exhausted by the following list. The right [ indicates the number of tilings) F 4 , 1] G 8 , 1] 12 , H 12 , 7] G 16 , TG 16 , H 16 , 3] MTG , H 20 , [5] . G 24 , TG 24 , H 24 , I 24 [5] F = 48 : F 48 , TF 48 , G 48 , TG 48 , H 48 , I 48 , 6] 60 , H 60 , TH 60 , 8] G 120 , TG 120 , H 120 , I 120 , T I 120 , 6] G 8n 4 , TG 8n 4 , MTG 8n 4 , MTG 8n 4 , H 8n 4 , TH 8n 4 , 6] F = 16n : G 16n , TG ....
....G 4n 2 (n 1) In the case F 0 (mod 4) such tilings are exhausted by the following list. The right [ indicates the number of tilings) F 4 , 1] G 8 , 1] 12 , H 12 , 7] G 16 , TG 16 , H 16 , 3] MTG , H 20 , 5] G 24 , TG 24 , H 24 , I 24 [5] F = 48 : F 48 , TF 48 , G 48 , TG 48 , H 48 , I 48 , 6] 60 , H 60 , TH 60 , 8] G 120 , TG 120 , H 120 , I 120 , T I 120 , 6] G 8n 4 , TG 8n 4 , MTG 8n 4 , MTG 8n 4 , H 8n 4 , TH 8n 4 , 6] F = 16n : G 16n , TG 16n , H 16n , I 16n , 4] ....
[Article contains additional citation context not shown here]
B. Grunbaum and G. C. Shephard, Spherical tilings with transitivity properties, in The Geometric Vein (ed. C. Davis, B. Grunbaum, F. A. Sherk), 65--98, Springer-Verlag, New York, 1981.
Escher Sphere Construction Kit - Yen, Séquin (2001) (Correct)
....done in the Escherization of images [11] 2.2 Spherical Tiling As with planar tiling, in spherical tiling we start with a basic shape and then modify it to create an interesting tessellation. Now, however, this basic shape must tile the sphere. Of the many possible spherical tiling schemes [8], in this paper we concentrate on the ones with the highest degree of truly three dimensional symmetries, the ones derived from the most regular polyhedra the five Platonic solids. To create an artistic tessellation based on a particular Platonic solid, we take the face shape of that solid, a ....
B. Grunbaum and G. C. Shepard. Spherical Tilings with Transitivity Properties. In C. Davis et al., editors, The Geometric Vein: The Coxeter Festschrift , pages 65--98. Springer-Verlag, New York, 1981.
Two-Dimensional Symmetry Mutation - Huson (Correct)
....This division is reinforced by the naming schemes that are generally used for their symmetry groups. In the Euclidean case, the 17 wall paper groups are known by their crystallographic names [Hah83] see Table 1, whereas in the spherical case, a number of different naming schemes are in use [GS81], see Table 2. None of the classical naming schemes generalize to the hyperbolic case. Moreover, the names themselves do not contain enough information to unambiguously determine the group that they denote, i.e. they are just pointers to full definitions in tables such as [Hah83] To obtain a ....
B. Grunbaum and G.C. Shephard, Spherical tilings with transitivity properties, Geometric Vein, Coxeter Festschrift (New York Heidelberg Berlin), Springer Verlag, New York Heidelberg Berlin, 1981.
Examples of Spherical Tilings By Congruent Quadrangles - Ueno, Agaoka (Correct)
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B. Grunbaum and G. C. Shephard, Spherical tilings with transitivity properties, in The Geometric Vein (ed. C. Davis, B. Grunbaum, F. A. Sherk), 65--98, Springer-Verlag, New York, 1981.
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