His work features mathematical objects and operations including impossible objects, explorations of infinity, reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. In the late twentieth century, he became more widely appreciated, and in the twenty-first century he has been celebrated in exhibitions across the world. He was 70 before a retrospective exhibition was held. Despite wide popular interest, Escher was for long somewhat neglected in the art world, even in his native Netherlands. These tessellations work because all the properties of a tessellation are present.Maurits Cornelis Escher was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Both tessellations will fill the plane, there are no gaps, the sum of the interior angle meeting at the vertex is 360 ∘, 360 ∘, and both are achieved by translation transformations. The interior angle of a hexagon is 120 ∘, 120 ∘, and the sum of three interior angles is 360 ∘. There are three hexagons meeting at each vertex. An interior angle of a square is 90 ∘Figure 10.103, the tessellation is made up of regular hexagons. There are four squares meeting at a vertex. In Figure 10.102, the tessellation is made up of squares. For a tessellation of regular congruent polygons, the sum of the measures of the interior angles that meet at a vertex equals 360 ∘.In other words, if you were to draw a circle around a vertex, it would include a corner of each shape touching at that vertex. All the shapes are joined at a vertex.
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