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 about GeometryIf 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 >A congruence statement generally follows the syntax, "Shape ABCD is congruent to shape WXYZ." This notation convention matches the sides and angles of the two shapes; therefore, side AB of the first shape corresponds to side WX of the second one. Similarly, the angle BCD, or simply C, corresponds to the angle XYZ or Y.
Full Answer >A 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 >The area of any simple shape, such as a circle, triangle or rectangle, can be found by taking a series of measurements from the shape and plugging them into a formula. The necessary formula varies according to the shape but works for all shapes of that type.
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