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6.AT.6. TESSELLATIONS
Albrecht Dürer. Underweysung der messung .... 1525 & 1538. Op. cit. in 6.AA. Figures 22 27 (pp. 156 169 in The Painter's Manual, Dürer's 1525 ff. E vi v   F-iii-v) show: the three regular tessellations; the quasi-regular one, 3636, and some of its dual; several irregular ones, including some partial tessellations with pentagons; and the truncated square lattice, 482. In the revised version of 1538, he adds some tilings by rhombuses (figures 23a & 24, pp. 410 411 in The Painter's Manual).

Albrecht Dürer. Elementorum Geometricorum (?). Op. cit. in 6.AA, 1532. Book II, fig. 22 27, pp. 62-67, is the material from the 1525 version.

J. Kepler. Letter to Herwart von Hohenberg. 6 Aug 1599. Op. cit. in 6.AT.2. Field, p. 105, says Kepler discusses tessellations here and this is the earliest of his writings to do so.

J. Kepler. Harmonices Mundi. 1619. Book II. Opp. cit. above. Prop. XVIII, p. 51 & plate (missing in my facsimile). Shows there are only three regular plane tessellations and mentions the dual of 3636, which is the 'baby blocks' tessellation. Prop. XIX XX, pp. 51 56 & four plates (three missing in my facsimile). Finds the 8 further Archimedean tessellations and 7 of the 10 further ways to fill 360 degrees with corners of regular polygons. He misses 3,7,42; 3,8,24; 3,9,18 despite computing, e.g., that a triangle and a heptagon would leave a gap of 40/21 of a right angle. Field, p. 109, notes that Kepler doesn't clearly have all vertices the same in some pictures -- e.g. he has both 3366 and 3636 patterns in his figure R.

Koloman Moser. Ver Sacrum. 1902. This Viennese art nouveau drawing is considered to be the first tessellation using life-like figures. It has trout and the pattern has symmetry (or wallpaper) group pg and isohedral type IH2.

Branko Grünbaum & G. C. Shephard. Tilings and Patterns. Freeman, 1986. I haven't examined this thoroughly yet, but it clearly is the definitive work and describes everything known to date.



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