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Yes, rotational symmetry of order 2.

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Q: A parallelogram has symmetry with respect to the point of intersection of its diagonals?
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What is reflectional summetry?

Reflection symmetry, reflectional symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection


Set of ordered pairs has point symmetry with respect to the origin 0 0?

circle


Why 5 fold rotation of lattice is not possible?

Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag (see opposite) has three rotational symmetries (or "a threefold rotational symmetry"). More examples may be seen below. The degree of rotational symmetry is how many degrees the shape has to be turned to look the same on a different side or vertex. It can not be the same side or vertex.Contents[hide] 1 Formal treatment 1.1 n-fold rotational symmetry1.2 Examples1.3 Multiple symmetry axes through the same point1.4 Rotational symmetry with respect to any angle1.5 Rotational symmetry with translational symmetry2 See also3 References4 External linksFormal treatmentFormally, rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore a symmetry group of rotational symmetry is a subgroup of E+(m) (see Euclidean group). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is homogeneous, and the symmetry group is the whole E(m). With the modified notion of symmetry for vector fields the symmetry group can also be E+(m).For symmetry with respect to rotations about a point we can take that point as origin. These rotations form the special orthogonal group SO(m), the group of m×m orthogonal matrices with determinant 1. For m=3 this is the rotation group SO(3).In another meaning of the word, the rotation group of an object is the symmetry group within E+(n), the group of direct isometries; in other words, the intersection of the full symmetry group and the group of direct isometries. For chiral objects it is the same as the full symmetry group.Laws of physics are SO(3)-invariant if they do not distinguish different directions in space. Because of Noether's theorem, rotational symmetry of a physical system is equivalent to the angular momentum conservation law. See also Rotational invariance.n-fold rotational symmetryRotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the nth order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of 360°/n (180°, 120°, 90°, 72°, 60°, 51 3/7 °, etc.) does not change the object. Note that "1-fold" symmetry is no symmetry, and "2-fold" is the simplest symmetry, so it does not mean "more than basic". The notation for n-fold symmetry is Cn or simply "n". The actual symmetry group is specified by the point or axis of symmetry, together with the n. For each point or axis of symmetry the abstract group type is cyclic group Zn of order n. Although for the latter also the notation Cn is used, the geometric and abstract Cn should be distinguished: there are other symmetry groups of the same abstract group type which are geometrically different, see cyclic symmetry groups in 3D.The fundamental domain is a sector of 360°/n.Examples without additional reflection symmetry:n = 2, 180°: the dyad[disambiguation needed ], quadrilaterals with this symmetry are the parallelograms; other examples: letters Z, N, S; apart from the colors: yin and yangn = 3, 120°: triad[disambiguation needed ], triskelion, Borromean rings; sometimes the term trilateral symmetry is used;n = 4, 90°: tetrad[disambiguation needed ], swastikan = 6, 60°: hexad, raelian symbol, new versionn = 8, 45°: octad, Octagonal muqarnas, computer-generated (CG), ceilingCn is the rotation group of a regular n-sided polygon in 2D and of a regular n-sided pyramid in 3D.If there is e.g. rotational symmetry with respect to an angle of 100°, then also with respect to one of 20°, the greatest common divisor of 100° and 360°.A typical 3D object with rotational symmetry (possibly also with perpendicular axes) but no mirror symmetry is a propeller.ExamplesC2 (more examples) Double Pendulum fractalThe starting position in shogiC3 (more examples) Roundabout traffic signSnoldelev Stone's interlocked drinking horns designC4 (more examples) Decorative Hindu form of the swastikaMultiple symmetry axes through the same pointFor discrete symmetry with multiple symmetry axes through the same point, there are the following possibilities: In addition to an n-fold axis, n perpendicular 2-fold axes: the dihedral groups Dn of order 2n(n≥2). This is the rotation group of a regular prism, or regular bipyramid. Although the same notation is used, the geometric and abstract Dn should be distinguished: there are other symmetry groups of the same abstract group type which are geometrically different, see dihedral symmetry groups in 3D.4×3-fold and 3×2-fold axes: the rotation group T of order 12 of a regular tetrahedron. The group is isomorphic to alternating group A4.3×4-fold, 4×3-fold, and 6×2-fold axes: the rotation group O of order 24 of a cube and a regular octahedron. The group is isomorphic to symmetric group S4.6×5-fold, 10×3-fold, and 15×2-fold axes: the rotation group I of order 60 of a dodecahedron and an icosahedron. The group is isomorphic to alternating group A5. The group contains 10 versions of D3 and 6 versions of D5(rotational symmetries like prisms and antiprisms).In the case of the Platonic solids, the 2-fold axes are through the midpoints of opposite edges, the number of them is half the number of edges. The other axes are through opposite vertices and through centers of opposite faces, except in the case of the tetrahedron, where the 3-fold axes are each through one vertex and the center of one face.Rotational symmetry with respect to any angleRotational symmetry with respect to any angle is, in two dimensions, circular symmetry. The fundamental domain is a half-line. In three dimensions we can distinguish cylindrical symmetry and spherical symmetry (no change when rotating about one axis, or for any rotation). That is, no dependence on the angle using cylindrical coordinates and no dependence on either angle using spherical coordinates. The fundamental domain is a half-plane through the axis, and a radial half-line, respectively. Axisymmetric or axisymmetrical are adjectives which refer to an object having cylindrical symmetry, or axisymmetry. An example of approximate spherical symmetry is the Earth (with respect to density and other physical and chemical properties).In 4D, continuous or discrete rotational symmetry about a plane corresponds to corresponding 2D rotational symmetry in every perpendicular plane, about the point of intersection. An object can also have rotational symmetry about two perpendicular planes, e.g. if it is the Cartesian product of two rotationally symmetry 2D figures, as in the case of e.g. the duocylinder and various regular duoprisms.Rotational symmetry with translational symmetryArrangement within a primitive cell of 2- and 4-fold rotocenters. A fundamental domain is indicated in yellow. 2-fold rotational symmetry together with single translational symmetry is one of the Frieze groups. There are two rotocenters per primitive cell.Together with double translational symmetry the rotation groups are the following wallpaper groups, with axes per primitive cell:p2 (2222): 4×2-fold; rotation group of a parallelogrammic, rectangular, and rhombic lattice.p3 (333): 3×3-fold; not the rotation group of any lattice (every lattice is upside-down the same, but that does not apply for this symmetry); it is e.g. the rotation group of the regular triangular tiling with the equilateral triangles alternatingly colored.p4 (442): 2×4-fold, 2×2-fold; rotation group of a square lattice.p6 (632): 1×6-fold, 2×3-fold, 3×2-fold; rotation group of a hexagonal lattice.2-fold rotocenters (including possible 4-fold and 6-fold), if present at all, form the translate of a lattice equal to the translational lattice, scaled by a factor 1/2. In the case translational symmetry in one dimension, a similar property applies, though the term "lattice" does not apply.3-fold rotocenters (including possible 6-fold), if present at all, form a regular hexagonal lattice equal to the translational lattice, rotated by 30° (or equivalently 90°), and scaled by a factorArrangement within a primitive cell of 2-, 3-, and 6-fold rotocenters, alone or in combination (consider the 6-fold symbol as a combination of a 2- and a 3-fold symbol); in the case of 2-fold symmetry only, the shape of the parallelogram can be different. For the case p6, a fundamental domain is indicated in yellow. 4-fold rotocenters, if present at all, form a regular square lattice equal to the translational lattice, rotated by 45°, and scaled by a factor6-fold rotocenters, if present at all, form a regular hexagonal lattice which is the translate of the translational lattice.Scaling of a lattice divides the number of points per unit area by the square of the scale factor. Therefore the number of 2-, 3-, 4-, and 6-fold rotocenters per primitive cell is 4, 3, 2, and 1, respectively, again including 4-fold as a special case of 2-fold, etc.3-fold rotational symmetry at one point and 2-fold at another one (or ditto in 3D with respect to parallel axes) implies rotation group p6, i.e. double translational symmetry and 6-fold rotational symmetry at some point (or, in 3D, parallel axis). The translation distance for the symmetry generated by one such pair of rotocenters is 2√3 times their distance.Hexakis triangular tiling, an example of p6 (with colors) and p6m (without); the lines are reflection axes if colors are ignored, and a special kind of symmetry axis if colors are not ignored: reflection reverts the colors. Rectangular line grids in three orientations can be distinguished.See alsoAmbigramAxial symmetryCrystallographic restriction theoremFrieze groupLorentz symmetryPoint groups in three dimensionsRecycling symbolReflection symmetryRotational invarianceScrew axisSpace groupSymmetry groupSymmetry combinationsThree haresTranslational symmetryWallpaper groupReferencesWeyl, Hermann (1982) [1952]. Symmetry. Princeton: Princeton University Press. ISBN 0-691-02374-3.External linksMedia related to Rotational symmetry by order at Wikimedia CommonsRotational Symmetry Examples from Math Is FunView page ratings Rate this pageRate this pagePage ratingsWhat's this?Current average ratings.TrustworthyObjectiveCompleteMissing most informationWell-writtenI am highly knowledgeable about this topic (optional)I have a relevant college/university degreeIt is part of my professionIt is a deep personal passionThe source of my knowledge is not listed hereI would like to help improve Wikipedia, send me an e-mail (optional)We will send you a confirmation e-mail. We will not share your e-mail address with outside parties as per our feedback privacy statement.Submit ratingsSaved successfullyYour ratings have not been submitted yetYour ratings have expiredPlease reevaluate this page and submit new ratings.An error has occured. Please try again later.Thanks! Your ratings have been saved.Please take a moment to complete a short survey.Start surveyMaybe laterThanks! Your ratings have been saved.Do you want to create an account?An account will help you track your edits, get involved in discussions, and be a part of the community.Create an accountorLog inMaybe laterThanks! 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What type of shape has planes of symmetry?

If a two-dimensional shape has a line of symmetry, the shape is also symmetrical with respect to the plane passing through that line and perpendicular to the plane of the shape. For example, the floor of a rectangular room is symmetrical about a vertical plane halfway along the length (or breadth) of the room. Some 3-dimensional shapes will also have planes of symmetry. A sphere has infinitely many. An ellipsoid has three - one each along two of its axes. A cuboid, similarly, has 3. A torus (doughnut) has one. A pyramid with a n-gon base will have n vertical planes, and so on.


What is the axis of symmetry of x2 plus 2x plus 6?

That will be a vertical line that passes through the parabola at the point where it's slope is equal to zero. The first step then, is to take the derivative of the curve with respect to x: y = x2 + 2x + 6 dy/dx = 2x + 2 Then let dy/dx equal zero, and solve for x: 0 = 2x + 2 2x = -2 x = -1 So the axis of symmetry is the line x = -1.

Related questions

Parallelogram has symmetry with respect to the line that bisects it vertically?

In general, no. Not unless the parallelogram has at least one right angle.


What is reflectional summetry?

Reflection symmetry, reflectional symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection


Set of ordered pairs has point symmetry with respect to the origin 0 0?

circle


What is true of an asymmetric carbon?

Every asymmetric carbon (also known as chiral carbon) atom has for different groups attached to it. Those molecules have no planes of symmetry or axes of symmetry with respect to chiral carbon atoms.


What is an intersected?

An intersection is the region of space that forms when two forms overlap (the intersection of two lines makes a point, the intersection of two planes makes a line, etc.). In set theory, it is the set formed when two or more sets overlap in terms of common elements. With respect to roads, it is the place where two roads cross each other.


How does a square differ from a rhombus?

A square is a rhombus with all angles 90o. When the angles of a rhombus are not all 90o, it differs from the square in this respect, and the diagonals are not of equal length unlike those of a square. A rhombus is like a square in that all its sides are equal in length, opposite sides are parallel and the diagonals are perpendicular and bisect each other.


What does a tatto star mean under the eye?

Other than nothing, this would stand for bad taste on the person who wears it with no regard for symmetry or a whole lot of self respect.


Why 5 fold rotation of lattice is not possible?

Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag (see opposite) has three rotational symmetries (or "a threefold rotational symmetry"). More examples may be seen below. The degree of rotational symmetry is how many degrees the shape has to be turned to look the same on a different side or vertex. It can not be the same side or vertex.Contents[hide] 1 Formal treatment 1.1 n-fold rotational symmetry1.2 Examples1.3 Multiple symmetry axes through the same point1.4 Rotational symmetry with respect to any angle1.5 Rotational symmetry with translational symmetry2 See also3 References4 External linksFormal treatmentFormally, rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore a symmetry group of rotational symmetry is a subgroup of E+(m) (see Euclidean group). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is homogeneous, and the symmetry group is the whole E(m). With the modified notion of symmetry for vector fields the symmetry group can also be E+(m).For symmetry with respect to rotations about a point we can take that point as origin. These rotations form the special orthogonal group SO(m), the group of m×m orthogonal matrices with determinant 1. For m=3 this is the rotation group SO(3).In another meaning of the word, the rotation group of an object is the symmetry group within E+(n), the group of direct isometries; in other words, the intersection of the full symmetry group and the group of direct isometries. For chiral objects it is the same as the full symmetry group.Laws of physics are SO(3)-invariant if they do not distinguish different directions in space. Because of Noether's theorem, rotational symmetry of a physical system is equivalent to the angular momentum conservation law. See also Rotational invariance.n-fold rotational symmetryRotational symmetry of order n, also called n-fold rotational symmetry, or discrete rotational symmetry of the nth order, with respect to a particular point (in 2D) or axis (in 3D) means that rotation by an angle of 360°/n (180°, 120°, 90°, 72°, 60°, 51 3/7 °, etc.) does not change the object. Note that "1-fold" symmetry is no symmetry, and "2-fold" is the simplest symmetry, so it does not mean "more than basic". The notation for n-fold symmetry is Cn or simply "n". The actual symmetry group is specified by the point or axis of symmetry, together with the n. For each point or axis of symmetry the abstract group type is cyclic group Zn of order n. Although for the latter also the notation Cn is used, the geometric and abstract Cn should be distinguished: there are other symmetry groups of the same abstract group type which are geometrically different, see cyclic symmetry groups in 3D.The fundamental domain is a sector of 360°/n.Examples without additional reflection symmetry:n = 2, 180°: the dyad[disambiguation needed ], quadrilaterals with this symmetry are the parallelograms; other examples: letters Z, N, S; apart from the colors: yin and yangn = 3, 120°: triad[disambiguation needed ], triskelion, Borromean rings; sometimes the term trilateral symmetry is used;n = 4, 90°: tetrad[disambiguation needed ], swastikan = 6, 60°: hexad, raelian symbol, new versionn = 8, 45°: octad, Octagonal muqarnas, computer-generated (CG), ceilingCn is the rotation group of a regular n-sided polygon in 2D and of a regular n-sided pyramid in 3D.If there is e.g. rotational symmetry with respect to an angle of 100°, then also with respect to one of 20°, the greatest common divisor of 100° and 360°.A typical 3D object with rotational symmetry (possibly also with perpendicular axes) but no mirror symmetry is a propeller.ExamplesC2 (more examples) Double Pendulum fractalThe starting position in shogiC3 (more examples) Roundabout traffic signSnoldelev Stone's interlocked drinking horns designC4 (more examples) Decorative Hindu form of the swastikaMultiple symmetry axes through the same pointFor discrete symmetry with multiple symmetry axes through the same point, there are the following possibilities: In addition to an n-fold axis, n perpendicular 2-fold axes: the dihedral groups Dn of order 2n(n≥2). This is the rotation group of a regular prism, or regular bipyramid. Although the same notation is used, the geometric and abstract Dn should be distinguished: there are other symmetry groups of the same abstract group type which are geometrically different, see dihedral symmetry groups in 3D.4×3-fold and 3×2-fold axes: the rotation group T of order 12 of a regular tetrahedron. The group is isomorphic to alternating group A4.3×4-fold, 4×3-fold, and 6×2-fold axes: the rotation group O of order 24 of a cube and a regular octahedron. The group is isomorphic to symmetric group S4.6×5-fold, 10×3-fold, and 15×2-fold axes: the rotation group I of order 60 of a dodecahedron and an icosahedron. The group is isomorphic to alternating group A5. The group contains 10 versions of D3 and 6 versions of D5(rotational symmetries like prisms and antiprisms).In the case of the Platonic solids, the 2-fold axes are through the midpoints of opposite edges, the number of them is half the number of edges. The other axes are through opposite vertices and through centers of opposite faces, except in the case of the tetrahedron, where the 3-fold axes are each through one vertex and the center of one face.Rotational symmetry with respect to any angleRotational symmetry with respect to any angle is, in two dimensions, circular symmetry. The fundamental domain is a half-line. In three dimensions we can distinguish cylindrical symmetry and spherical symmetry (no change when rotating about one axis, or for any rotation). That is, no dependence on the angle using cylindrical coordinates and no dependence on either angle using spherical coordinates. The fundamental domain is a half-plane through the axis, and a radial half-line, respectively. Axisymmetric or axisymmetrical are adjectives which refer to an object having cylindrical symmetry, or axisymmetry. An example of approximate spherical symmetry is the Earth (with respect to density and other physical and chemical properties).In 4D, continuous or discrete rotational symmetry about a plane corresponds to corresponding 2D rotational symmetry in every perpendicular plane, about the point of intersection. An object can also have rotational symmetry about two perpendicular planes, e.g. if it is the Cartesian product of two rotationally symmetry 2D figures, as in the case of e.g. the duocylinder and various regular duoprisms.Rotational symmetry with translational symmetryArrangement within a primitive cell of 2- and 4-fold rotocenters. A fundamental domain is indicated in yellow. 2-fold rotational symmetry together with single translational symmetry is one of the Frieze groups. There are two rotocenters per primitive cell.Together with double translational symmetry the rotation groups are the following wallpaper groups, with axes per primitive cell:p2 (2222): 4×2-fold; rotation group of a parallelogrammic, rectangular, and rhombic lattice.p3 (333): 3×3-fold; not the rotation group of any lattice (every lattice is upside-down the same, but that does not apply for this symmetry); it is e.g. the rotation group of the regular triangular tiling with the equilateral triangles alternatingly colored.p4 (442): 2×4-fold, 2×2-fold; rotation group of a square lattice.p6 (632): 1×6-fold, 2×3-fold, 3×2-fold; rotation group of a hexagonal lattice.2-fold rotocenters (including possible 4-fold and 6-fold), if present at all, form the translate of a lattice equal to the translational lattice, scaled by a factor 1/2. In the case translational symmetry in one dimension, a similar property applies, though the term "lattice" does not apply.3-fold rotocenters (including possible 6-fold), if present at all, form a regular hexagonal lattice equal to the translational lattice, rotated by 30° (or equivalently 90°), and scaled by a factorArrangement within a primitive cell of 2-, 3-, and 6-fold rotocenters, alone or in combination (consider the 6-fold symbol as a combination of a 2- and a 3-fold symbol); in the case of 2-fold symmetry only, the shape of the parallelogram can be different. For the case p6, a fundamental domain is indicated in yellow. 4-fold rotocenters, if present at all, form a regular square lattice equal to the translational lattice, rotated by 45°, and scaled by a factor6-fold rotocenters, if present at all, form a regular hexagonal lattice which is the translate of the translational lattice.Scaling of a lattice divides the number of points per unit area by the square of the scale factor. Therefore the number of 2-, 3-, 4-, and 6-fold rotocenters per primitive cell is 4, 3, 2, and 1, respectively, again including 4-fold as a special case of 2-fold, etc.3-fold rotational symmetry at one point and 2-fold at another one (or ditto in 3D with respect to parallel axes) implies rotation group p6, i.e. double translational symmetry and 6-fold rotational symmetry at some point (or, in 3D, parallel axis). The translation distance for the symmetry generated by one such pair of rotocenters is 2√3 times their distance.Hexakis triangular tiling, an example of p6 (with colors) and p6m (without); the lines are reflection axes if colors are ignored, and a special kind of symmetry axis if colors are not ignored: reflection reverts the colors. Rectangular line grids in three orientations can be distinguished.See alsoAmbigramAxial symmetryCrystallographic restriction theoremFrieze groupLorentz symmetryPoint groups in three dimensionsRecycling symbolReflection symmetryRotational invarianceScrew axisSpace groupSymmetry groupSymmetry combinationsThree haresTranslational symmetryWallpaper groupReferencesWeyl, Hermann (1982) [1952]. Symmetry. Princeton: Princeton University Press. ISBN 0-691-02374-3.External linksMedia related to Rotational symmetry by order at Wikimedia CommonsRotational Symmetry Examples from Math Is FunView page ratings Rate this pageRate this pagePage ratingsWhat's this?Current average ratings.TrustworthyObjectiveCompleteMissing most informationWell-writtenI am highly knowledgeable about this topic (optional)I have a relevant college/university degreeIt is part of my professionIt is a deep personal passionThe source of my knowledge is not listed hereI would like to help improve Wikipedia, send me an e-mail (optional)We will send you a confirmation e-mail. We will not share your e-mail address with outside parties as per our feedback privacy statement.Submit ratingsSaved successfullyYour ratings have not been submitted yetYour ratings have expiredPlease reevaluate this page and submit new ratings.An error has occured. Please try again later.Thanks! Your ratings have been saved.Please take a moment to complete a short survey.Start surveyMaybe laterThanks! Your ratings have been saved.Do you want to create an account?An account will help you track your edits, get involved in discussions, and be a part of the community.Create an accountorLog inMaybe laterThanks! Your ratings have been saved.Did you know that you can edit this page?Edit this pageMaybe laterPersonal toolsLog in / create accountNamespacesArticleTalkVariantsViewsReadEditView historyActionsSearchNavigationMain pageContentsFeatured contentCurrent eventsRandom articleDonate to WikipediaInteractionHelpAbout WikipediaCommunity portalRecent changesContact WikipediaToolboxWhat links hereRelated changesUpload fileSpecial pagesPermanent linkCite this pageRate this pagePrint/exportCreate a bookDownload as PDFPrintable versionLanguagesالعربيةEsperantoفارسیFrançaisNederlandsРусскийSvenskaTürkçeThis page was last modified on 9 March 2012 at 06:59.Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. See Terms of use for details. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.Contact usPrivacy policyAbout WikipediaDisclaimersMobile view


What parts of the body are bilateral?

In bilateral symmetry (also called plane symmetry), only one plane, called the sagittal plane, will divide an organism into roughly mirror image halves (with respect to external appearance only, see situs solitus). Thus there is approximate reflection symmetry. Often the two halves can meaningfully be referred to as the right and left halves, e.g. in the case of an animal with a main direction of motion in the plane of symmetry.


Does a kite have a point symmetry?

It depend on what kind of kite you have. Two points are symmetric with respect to a point iff it is the midpoint of the line segment joining them. So if you have like a dragon kite, then probably not, but if you have a traditional dizmond kite, then yes.


With respect to or in respect of?

- in respect of chiefly British : with respect to : concerning - in respect to: with respect to : concerning - with respect to : with reference to : in relation to


Is it respect to or respect for?

respect for