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  2. Parabola - Wikipedia

    en.wikipedia.org/wiki/Parabola

    The point E is an arbitrary point on the parabola. The focus is F, the vertex is A (the origin), and the line FA is the axis of symmetry. The line EC is parallel to the axis of symmetry, intersects the x axis at D and intersects the directrix at C. The point B is the midpoint of the line segment FC.

  3. Symmetry (geometry) - Wikipedia

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

    The axis of symmetry of a two-dimensional figure is a line such that, if a perpendicular is constructed, any two points lying on the perpendicular at equal distances from the axis of symmetry are identical. Another way to think about it is that if the shape were to be folded in half over the axis, the two halves would be identical as mirror ...

  4. Symmetry operation - Wikipedia

    en.wikipedia.org/wiki/Symmetry_operation

    In mathematics, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out. For example, a 1 ⁄ 3 turn rotation of a regular triangle about its center, a reflection of a square across its diagonal, a translation of the Euclidean plane, or a point reflection of a sphere through its center are all symmetry operations.

  5. Symmetry in mathematics - Wikipedia

    en.wikipedia.org/wiki/Symmetry_in_mathematics

    Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object

  6. Screw axis symmetry - Wikipedia

    en.wikipedia.org/wiki/Screw_axis

    In crystallography, a screw axis symmetry is a combination of rotation about an axis and a translation parallel to that axis which leaves a crystal unchanged. If φ = ⁠ 360° / n ⁠ for some positive integer n, then screw axis symmetry implies translational symmetry with a translation vector which is n times that of the screw displacement.

  7. Axis–angle representation - Wikipedia

    en.wikipedia.org/wiki/Axis–angle_representation

    The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...

  8. Tetrahedral symmetry - Wikipedia

    en.wikipedia.org/wiki/Tetrahedral_symmetry

    It is also the symmetry of a pyritohedron, which is extremely similar to the cube described, with each rectangle replaced by a pentagon with one symmetry axis and 4 equal sides and 1 different side (the one corresponding to the line segment dividing the cube's face); i.e., the cube's faces bulge out at the dividing line and become narrower there.

  9. Cyclic symmetry in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Cyclic_symmetry_in_three...

    It has reflection symmetry with respect to a plane perpendicular to the n-fold rotation axis. C nv, [n], (*nn) of order 2n - pyramidal symmetry or full acro-n-gonal group (abstract group Dih n); in biology C 2v is called biradial symmetry. For n=1 we have again C s (1*). It has vertical mirror planes. This is the symmetry group for a regular n ...