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A parallelogon is constructed by two or three pairs of parallel line segments. ... Every convex parallelogon is a zonogon, but hexagonal parallelogons enable the ...
An example of a convex polygon: a regular pentagon. In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). [1]
Every parallelohedron is a stereohedron, a convex polyhedron that tiles space in such a way that there exist symmetries of the tiling that take any other tile. A plesiohedron is a related class of three-dimensional space-filling polyhedra, formed from the Voronoi diagrams of periodic sets of points. [ 14 ]
Regular polyhedron. Platonic solid: . Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot ...
Conway was likely inspired by Martin Gardner's July 1975 column in Scientific American that discussed which convex polygons can tile the plane. [6] In August 1975, Gardner revealed that Conway had discovered his criterion while trying to find an efficient way to determine which of the 108 heptominoes tile the plane.
A pentagon is a five-sided polygon. A regular pentagon has 5 equal edges and 5 equal angles. In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.
Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 20th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three.
§9.1 Tilings by polygons, triangular tiling, quadrilteral tiling, pentagonal tiling, hexagonal tiling, parallelogon, §9.2 non-convex polygon tilings, ...