the "base" of the triangle is one side of the polygon.We can learn a lot about regular polygons by breaking them into triangles like this: Take half a heptagon (tessellated by seven of the small triangles) to the. (Not all polygons have those properties, but triangles and regular polygons do). Platonically tessellated Riemann surfaces and the structure of triangle groups. The radius of the incircle is the apothem of the polygon. The "inside" circle is called an incircle and it just touches each side of the polygon at its midpoint. The radius of the circumcircle is also the radius of the polygon. The "outside" circle is called a circumcircle, and it connects all vertices (corner points) of the polygon. Sounds quite musical if you repeat it a few times, but they are just the names of the "outer" and "inner" circles (and each radius) that can be drawn on a polygon like this: The hyperbolic plane is another matter, here is a tesselation that includes regular heptagons. covers a surface without any gaps or overlaps and can be extended in the plane infinitely. Example: What are the interior and exterior angles of a regular hexagon?Īnd now for some names: "Circumcircle, Incircle, Radius and Apothem. A key in finding a tessellation with copies of a triangle is to experiment with organizing copies of the triangle, and then reasoning that two copies of a triangle can always be arranged to form a parallelogram. What is Heptagonal Tessellation Heptagonal Tessellation is a pattern of seven sided polygon that completely.
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