Tessellations occur when a shape is repeated in an interlocking pattern that fully covers a flat surface, or plane, like the pieces of a puzzle. Some shapes cannot tessellate because they are not regular polygons or do not contain vertices (corner points). They therefore cannot be arranged on a plane without overlapping or leaving some space uncovered. Due to its rounded edges and lack of vertices, the circle is normally not tessellated.
Three main categories of tessellations exist: regular, semi-regular and demi. The three regular tessellations use one repeating polygon that produces an identical pattern at each vertex. Regular tessellations are constructed with triangles, squares or hexagons. The tessellations are named according to the number of sides in each intersecting shape. For example, a pattern of four lines intersecting at right angles is a 4.4.4.4 tessellation.
The eight semi-regular tessellations are composed of two or more regular polygons. They use the following combinations of shapes:
Like regular tessellations, the pattern at each vertex is the same. However, because more than one shape is used, the pattern will contain more than one number. A pattern using triangles and hexagons is a 3.3.3.3.6 tessellation because four triangles and one hexagon meet at each vertex. Controversy exists between mathematicians regarding the definition of demi tessellations. These patterns do not follow normal rules of constructing a tessellation and may contain irregular polygons, curved shapes, and non-identical vertices.
Learn MoreA triangular-based pyramid is a convex solid figure with a base in the shape of a triangle and triangular sides that meet at points called vertices, according to New South Wales Board of Studies. Convex means that all its interior angles are less than or equal to 180 degrees.
Full Answer >A geometrical translation moves or slides a shape a fixed distance without rotating it, resizing it or performing any other sort of transformation to it. Translations move every point within the shape the same distance and preserve the geometrical properties of the original shape.
Full Answer >To calculate area, first determine the shape of the object. Next, apply the correct formula is needed, and substitute the values into the appropriate places. Finally, the equation should be solved to find the number that represents the area.
Full Answer >To find the perimeter of a trapezoid, add up the length of each of the sides of the shape. Use the equation P = a + b + c + d.
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