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  2. Symmetry (geometry) - Wikipedia

    en.wikipedia.org/wiki/Symmetry_(geometry)

    if the rotation angle has no common divisor with 360°, the symmetry group is not discrete. if the rotoreflection has a 2n-fold rotation angle (angle of 180°/n), the symmetry group is S 2n of order 2n (not to be confused with symmetric groups, for which the same notation is used; the abstract group is C 2n).

  3. Spherical lune - Wikipedia

    en.wikipedia.org/wiki/Spherical_lune

    Common examples of great circles are lines of longitude (meridians) on a sphere, which meet at the north and south poles. A spherical lune has two planes of symmetry. It can be bisected into two lunes of half the angle, or it can be bisected by an equatorial line into two right spherical triangles.

  4. Rectangle - Wikipedia

    en.wikipedia.org/wiki/Rectangle

    It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°). Other rectangles A saddle rectangle has 4 nonplanar vertices, alternated from vertices of a rectangular cuboid , with a unique minimal surface interior defined as a linear combination of the four vertices, creating a saddle surface.

  5. Symmetry - Wikipedia

    en.wikipedia.org/wiki/Symmetry

    The type of symmetry is determined by the way the pieces are organized, or by the type of transformation: An object has reflectional symmetry (line or mirror symmetry) if there is a line (or in 3D a plane) going through it which divides it into two pieces that are mirror images of each other. [6]

  6. Rotational symmetry - Wikipedia

    en.wikipedia.org/wiki/Rotational_symmetry

    Rotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the n th order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of ⁠ ⁠ (180°, 120°, 90°, 72°, 60°, 51 3 ⁄ 7 °, etc.) does not change the object. A "1-fold" symmetry is no symmetry (all ...

  7. Kite (geometry) - Wikipedia

    en.wikipedia.org/wiki/Kite_(geometry)

    Because of this symmetry, a kite has two equal angles and two pairs of adjacent equal-length sides. Kites are also known as deltoids, [1] but the word deltoid may also refer to a deltoid curve, an unrelated geometric object sometimes studied in connection with quadrilaterals. [2] [3] A kite may also be called a dart, [4] particularly if it is ...

  8. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    A parallelogram has rotational symmetry of order 2 (through 180°) (or order 4 if a square). If it also has exactly two lines of reflectional symmetry then it must be a rhombus or an oblong (a non-square rectangle). If it has four lines of reflectional symmetry, it is a square.

  9. Isosceles triangle - Wikipedia

    en.wikipedia.org/wiki/Isosceles_triangle

    In geometry, an isosceles triangle (/ aɪ ˈ s ɒ s ə l iː z /) is a triangle that has two sides of equal length or two angles of equal measure. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.