Glossary

This glossary includes definitions and examples of basic terms. Please resize this window so that it is narrow, and keep it visible on your screen. It will be very helpful as you browse the site.

 

Angle: the figure formed by two line segments meeting at a point; also refers to the space between such lines

 

Axis: a reference line used by a transformation such as a reflection
	here, the dotted line is an axis of reflection—the line over which the shape has been reflected

 

Centroid: the "center-of-balance" of a polygon or shape; for regular polygons, the centroid is the center of the circle that could be inscribed in (drawn to fit inside) or circumscribed around (drawn to fit outside) the regular polygon

 

in black is the original tessellation; in orange are the lines drawn from the vertices through the centroids Centroid Technique: a technique for modifying existing tessellations that involves doing the following for each polygon in a tessellation: drawing a line from each vertex to or through the centroid of the polygon

 

Congruent: the property of being identical in form, shape, and size; two figures are congruent if they can be made exactly alike through transformations

(Note: Although the terms congruent and symmetry are very similar, congruent refers more to the property of being identical, while symmetry refers more to the means by which two shapes can be shown to be identical.)

 

Cool Color: a mostly bluish or greenish color; tends to be seen further away from the eye than warm colors

 

Degree: unit of measure for angles; amount of rotation needed to match one line segment of an angle onto the other

 

Demiregular Tessellation: a tessellation composed of more than one type of regular polygon such that exactly two or three polygon arrangements exist; there are fourteen semiregular tessellations

Shown here is the 3.12.12, 3.4.3.12 demiregular tessellation; notice that the polygon arrangement at point 1 is 3.12.12, while the polygon arrangement at point 2 is 3.4.3.12

 

two possible diagonals Diagonal: a line between two vertices of a polygon that is not also a side of the polygon

 

in black is the original tessellation of quadrilaterals; in orange are the diagonals of each and every quadrilateral Diagonal Technique: a technique for modifying existing tessellations that involves drawing the diagonals of each polygon in a tessellation

 

Distinct: different; two objects are distinct if they are not identical

 

the change indicated in orange is applied at the bottom of the tessellation (look carefully) Division: a technique for modifying tessellations that involves dividing a certain shape into smaller shapes; this modification is repeated throughout the tessellation

 

Dual: the tessellation formed by connecting the centroids of adjacent shapes of an existing tessellation (the orange and black tessellations are duals of each other)

 

Equilateral Triangle: a triangle (three-sided polygon) with sides of equal lengths and angles of equal measure)

 

Glide Reflection: a transformation performed by a reflection and a translation. Whether the reflection or translation comes first does not matter.

 

Glide Reflectional Symmetry: symmetry when obtained by a glide reflection (animated)

 

Grids: treating tessellations as simple outlines; overlapping, rotating, and other similar modifications of grids can result in new tessellations

 

Heptagon: a polygon with seven sides; shown here is a regular heptagon which has sides of equal length and angles of equal measure

 

Hexagon: a polygon with six sides; shown here is a regular hexagon which has sides of equal length and angles of equal measure; regular hexagons are very common in regular, semiregular, and demiregular tessellations

 

Interior Angle: an angle facing the interior or inside of a polygon or shape

 

the change indicated in orange is applied at the bottom of the tessellation (look carefully) Joining: a technique for modifying tessellations that involves joining several adjacent shapes into a larger shape; this modification is repeated throughout the tessellation

 

a straight line Line: the path traced by a moving point; in tessellations, "line" usually refers to straight lines

 

Midpoint: the point on a line that is the same distance from each endpoint of the line

 

inside of each black polygon, there is an orange polygon formed by joining the midpoints of adjacent sides of the original black polygon Midpoint Technique: a technique for modifying existing tessellations that involves joining the midpoints of adjacent sides of each polygon in a tessellation

 

Octagon: a polygon with eight sides; shown here is a regular octagon which has sides of equal length and angles of equal measure

 

Offset Polygons: a technique for creating new tessellations that involves placing copies of a shape such that the sides and vertices do not align—in other words, the shapes are offset

 

Offset Technique: a technique for modifying tessellations that involves moving rows or columns of shapes independently of the rest of the tessellation

 

this pattern is not a tessellation because it is not composed of distinct shapes Pattern: repeating figure; all tessellations are patterns because they repeat, but not all patterns are tessellations

 

Pentagon: a polygon with five sides; shown here is a regular pentagon which has sides of equal length and angles of equal measure

 

Point: a geometric object that has no length, width, nor breadth and that exists to define location; we represent points as dots:

 

Polygon: a closed figure bounded by three or more straight line segments

 

Quadrilateral: a polygon with four sides; squares and rhombi are two important types of quadrilaterals

 

Reflection: a transformation performed by plotting corresponding points on the opposite side of an axis of reflection. A corresponding point must be the same distance from the axis as its original point.

 

Reflectional Symmetry: symmetry when obtained by a reflection

 

Regular Polygons: polygons that have sides of equal lengths and angles of equal measures

 

shown here is the 3.3.3.3.3.3 regular tessellation Regular Tessellation: a tessellation composed of only one type of regular polygon; the arrangement of polygons at every point is the same; three regular tessellations exist: 3.3.3.3.3.3, 4.4.4.4, 6.6.6

 

Rhombus: a quadrilateral (polygon with four sides) that has sides of equal lengths

 

Rotation: a transformation performed by turning a shape around a point. This point is called a center of rotation.

 

in orange is the rotated group of shapes; this change can be applied to the other similarly-shaped groups of shapes of the tessellation Rotation Technique: a technique for modifying tessellations that involves rotating a group of shapes without disturbing the rest of the tessellation; this rotation is usually repeated throughout the tessellation

 

Rotational Symmetry: symmetry when obtained by a rotation (animated)

 

shown here is the 4.8.8 semiregular tessellation Semiregular Tessellation: a tessellation composed of more than one type of regular polygon such that the polygon arrangement at every vertex is the same; eight semiregular tessellations exist

 

Shape: a closed figure or form; has a definite interior (inside) and exterior (outside)

 

Square: a quadrilateral (polygon with four sides) with sides of equal lengths and angles of exactly 90 degrees

 

reflectional symmetry is shown here; the black and orange shapes are identical Symmetry: the property of being identical in form and configuration usually across a line or point

(Note: Although the terms congruent and symmetry are very similar, congruent refers more to the property of being identical, while symmetry refers more to the means by which two shapes can be shown to be identical.)

 

Tessellation: a repeating pattern of distinct shapes (see the Gallery or any part of the site for examples)

 

the black shape has been rotated and reflected to create the orange shape—both actions are examples of transformations Transformation: a method of changing one set of points into another; three transformations important to tessellations are reflection, rotation, translation, and glide reflection

 

Translation: a transformation performed by simply moving a shape

 

Translational Symmetry: symmetry when obtained by a translation

 

Trapezoid: a quadrilateral (polygon with four sides) that has two parallel sides

 

Triangle: a polygon with three sides; an important type of triangle is the equilateral triangle which is used in many regular, semiregular, and demiregular tesellations

 

in orange is the unit square; in black is the pattern that is duplicated Unit Cells: a technique for creating new tessellations that involves drawing a design within a square, equilateral triangle, or other simple figure, and duplicating this pattern in the simple grid-like fashion suggested by its outline

 

Value: the level of brightness of a color

 

Vertex: a point at which two line segments meet; usually associated with an angle

 

Warm Color: a mostly reddish or yellowish color; tends to be seen closer to the eye than cool colors

 

Totally Tessellated @ http://library.advanced.org/16661/