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A 3D-printed version of the Reutersvärd Triangle illusion. M.C. Escher's lithograph Waterfall (1961) depicts a watercourse that flows in a zigzag along the long sides of two elongated Penrose triangles, so that it ends up two stories higher than it began. The resulting waterfall, forming the short sides of both triangles, drives a water wheel.
Penrose triangle, an impossible figure whose boundary appears to wrap around it in a Möbius strip; Ribbon theory, the mathematical theory of infinitesimally thin strips that follow knotted space curves; Smale–Williams attractor, a fractal formed by repeatedly thickening a space curve to a Möbius strip and then replacing it with the boundary ...
Figure 2. The pentagonal Penrose tiling (P1) drawn in black on a colored rhombus tiling (P3) with yellow edges. [15] The first Penrose tiling (tiling P1 below) is an aperiodic set of six prototiles, introduced by Roger Penrose in a 1974 paper, [16] based on pentagons rather than squares.
The Penrose stairs were created by Lionel Penrose and his son Roger Penrose. [3] A variation on the Penrose triangle , it is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher.
Necker cube = reversible figure Penrose triangle = unrealizable object Kanizsa triangle = illusory contours. Visual illusions proper should be distinguished from some related phenomena. Some simple targets such as the Necker cube are capable of more than one interpretation, which are usually seen in alternation, one at a time. They may be ...
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
Octahectogon - 800 sides; Enneahectogon - 900 sides; Chiliagon - 1,000 sides; Myriagon - 10,000 sides; Megagon - 1,000,000 sides; Star polygon – there are multiple types of stars Pentagram - star polygon with 5 sides; Hexagram – star polygon with 6 sides Star of David (example) Heptagram – star polygon with 7 sides; Octagram – star ...
Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.