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.
Know MoreThree 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 more in GeometryA 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 >If a shape or image can be rotated less than 360 degrees and still retain the same appearance, this shape has rotational symmetry. For example, a five-pointed star can be turned to allow a different point to face upward and still appear as a five-pointed star; that's because this shape has rotational symmetry.
Full Answer >The cubic feet formula depends on the shape of the object for which one is calculating volume, but for a cube, v=a^3, where a is the length of one side in feet. For cylinders and prisms, the formula is the area of the base multiplied by the height.
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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