![[Left] Normal Streptocarpus flower (zygomorphic or mirror-symmetric), and [right] peloric (radially symmetric) flower on the same plant Peloria in Streptocarpus.jpg](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Peloria_in_Streptocarpus.jpg/330px-Peloria_in_Streptocarpus.jpg)
Floral symmetry describes whether, and how, a flower, in particular its perianth, can be divided into two or more identical or mirror-image parts.
Uncommonly, flowers may have no axis of symmetry at all, typically because their parts are spirally arranged.
Most flowers are actinomorphic ("star shaped", "radial"), meaning they can be divided into 3 or more identical sectors which are related to each other by rotation about the center of the flower. Typically, each sector might contain one tepal or one petal and one sepal and so on. It may or may not be possible to divide the flower into symmetrical halves by the same number of longitudinal planes passing through the axis: Oleander is an example of a flower without such mirror planes. Actinomorphic flowers are also called radially symmetrical or regular flowers. Other examples of actinomorphic flowers are the lily ( Lilium , Liliaceae) and the buttercup ( Ranunculus , Ranunculaceae).
Zygomorphic ("yoke shaped", "bilateral" – from the Greek ζυγόν, zygon, yoke, and μορφή, morphe, shape) flowers can be divided by only a single plane into two mirror-image halves, much like a yoke or a person's face. Examples are orchids and the flowers of most members of the Lamiales (e.g., Scrophulariaceae and Gesneriaceae). Some authors prefer the term monosymmetry or bilateral symmetry. [1] The asymmetry allows pollen to be deposited in specific locations on pollinating insects and this specificity can result in evolution of new species. [2]
Globally and within individual networks, zygomorphic flowers are a minority. Plants with zygomorphic flowers have smaller number of visitor species compared to those with actinomorphic flowers. Sub-networks of plants with zygomorphic flowers share greater connectance, greater asymmetry and lower coextinction robustness for both the plants and the visitor species. Plant taxa with zygomorphic flowers can have a greater risk of extinction due to pollinator decline. [3]
A few plant species have flowers lacking any symmetry, and therefore having a "handedness". Examples: Valeriana officinalis and Canna indica . [4]
Actinomorphic flowers are a basal angiosperm character; zygomorphic flowers are a derived character that has evolved many times. [5]
Some familiar and seemingly actinomorphic so-called flowers, such as those of daisies and dandelions (Asteraceae), and most species of Protea , are actually clusters of tiny (not necessarily actinomorphic) flowers arranged into a roughly radially symmetric inflorescence of the form known as a head, capitulum, or pseudanthium.
Peloria or a peloric flower is the aberration in which a plant that normally produces zygomorphic flowers produces actinomorphic flowers instead. This aberration can be developmental, or it can have a genetic basis: the CYCLOIDEA gene controls floral symmetry. Peloric Antirrhinum plants have been produced by knocking out this gene. [5] Many modern cultivars of Sinningia speciosa ("gloxinia") have been bred to have peloric flowers as they are larger and showier than the normally zygomorphic flowers of this species.
Charles Darwin explored peloria in Antirrhinum (snapdragon) while researching the inheritance of floral characteristics for his The Variation of Animals and Plants Under Domestication . [6] Later research, using Digitalis purpurea , showed that his results [7] were largely in line with Mendelian theory. [8]
If considering only those flowers which consist of a single flower, rather than a flower head or other form of inflorescence, their symmetries can be categorized into a relatively small number of two-dimensional symmetry groups. These groups are characterized by two types of symmetries: reflection (or mirror) symmetries, and rotational symmetries. Figures that are left invariant under reflections about a single axis have reflection symmetry, which is described by the cyclic group of order 2, (sometimes denoted ). Figures that are left invariant under rotations by have a rotational symmetry belonging to the cyclic group of order , (or ). Many flowers that are invariant under rotations by are also invariant under reflections about distinct axes, the combination of these two symmetries forms the larger dihedral group of dimension , (which has order ).
Flowers with bilateral symmetry, such as orchids have reflection symmetry about a single axis and no rotational symmetry, meaning that they are described simply by the reflection group .
Monocots are identifiable by their trimerous petals, meaning that they are often invariant under rotations by and thus have rotational symmetry. Monocots that exhibit rotational symmetry but not mirror symmetry (for instance, if their petals exhibit chirality) are described by the cyclic group of order 3, , and monocots with both rotational symmetry and reflection symmetry about 3 axes are described by the dihedral group of dimension 3, .
Eudicots with tetramerous or pentamerous petals are often invariant under rotations by or . Again, whether they also have mirror planes decides whether they belong to dihedral ( and ) or cyclic groups ( or ). Most eudiocots will have or symmetry, but, as was the case with monocots, those that exhibit chirality will only have cyclic symmetry of order the number of petals. For example, the individual petals of flowers in the genus Hypericum have no axis under which they are invariant under reflections, so their symmetry is described by .
There is the trend that, in general, the order of the cyclic group or dimension of the dihedral group that describes a flower's symmetry will correspond to the merosity of its petals. However, the sepals of some monocot flowers develop to replicate the petals, thus, superficially, certain monocots can appear to have rotational symmetry of order 6 and belong to either symmetry group or . Some composite flowers may also have at least a superficial cyclical or dihedral symmetry. How exact this symmetry is depends on the structure of the head of the flower. Even in monocots and eudicots, flower symmetries are rarely perfect, as any imperfections in the petals will result in imperfect invariance under rotations or reflections.
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object X is G = Sym(X).
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry.
In group theory, a dicyclic group (notation Dicn or Q4n, ⟨n,2,2⟩) is a particular kind of non-abelian group of order 4n (n > 1). It is an extension of the cyclic group of order 2 by a cyclic group of order 2n, giving the name di-cyclic. In the notation of exact sequences of groups, this extension can be expressed as:
Petals are modified leaves that surround the reproductive parts of flowers. They are often brightly colored or unusually shaped to attract pollinators. All of the petals of a flower are collectively known as the corolla. Petals are usually accompanied by another set of modified leaves called sepals, that collectively form the calyx and lie just beneath the corolla. The calyx and the corolla together make up the perianth, the non-reproductive portion of a flower. When the petals and sepals of a flower are difficult to distinguish, they are collectively called tepals. Examples of plants in which the term tepal is appropriate include genera such as Aloe and Tulipa. Conversely, genera such as Rosa and Phaseolus have well-distinguished sepals and petals. When the undifferentiated tepals resemble petals, they are referred to as "petaloid", as in petaloid monocots, orders of monocots with brightly colored tepals. Since they include Liliales, an alternative name is lilioid monocots.
In mathematics, a frieze or frieze pattern is a two-dimensional design that repeats in one direction. Such patterns occur frequently in architecture and decorative art. Frieze patterns can be classified into seven types according to their symmetries. The set of symmetries of a frieze pattern is called a frieze group.
In geometry, a myriagon or 10000-gon is a polygon with 10000 sides. Several philosophers have used the regular myriagon to illustrate issues regarding thought.
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.
In geometry, a triacontagon or 30-gon is a thirty-sided polygon. The sum of any triacontagon's interior angles is 5040 degrees.
In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the order in which they are taken, but different orderings produce conjugate elements, which have the same order. This order is known as the Coxeter number. They are named after British-Canadian geometer H.S.M. Coxeter, who introduced the groups in 1934 as abstractions of reflection groups.
In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space. The symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent copies of a regular polytope is necessarily a reflection group. Reflection groups also include Weyl groups and crystallographic Coxeter groups. While the orthogonal group is generated by reflections, it is a continuous group, not a discrete group, and is generally considered separately.
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries.
In geometry, a two-dimensional point group or rosette group is a group of geometric symmetries (isometries) that keep at least one point fixed in a plane. Every such group is a subgroup of the orthogonal group O(2), including O(2) itself. Its elements are rotations and reflections, and every such group containing only rotations is a subgroup of the special orthogonal group SO(2), including SO(2) itself. That group is isomorphic to R/Z and the first unitary group, U(1), a group also known as the circle group.
In mathematics, the infinite dihedral group Dih∞ is an infinite group with properties analogous to those of the finite dihedral groups.
In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise.
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. Each symmetry operation is performed with respect to some symmetry element.
In geometry, a point reflection is a transformation of affine space in which every point is reflected across a specific fixed point. When dealing with crystal structures and in the physical sciences the terms inversion symmetry, inversion center or centrosymmetric are more commonly used.
In mathematics, a hyperoctahedral group is an important type of group that can be realized as the group of symmetries of a hypercube or of a cross-polytope. It was named by Alfred Young in 1930. Groups of this type are identified by a parameter n, the dimension of the hypercube.
In geometry, Coxeter notation is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram, with modifiers to indicate certain subgroups. The notation is named after H. S. M. Coxeter, and has been more comprehensively defined by Norman Johnson.
Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in the application of Quantum Mechanics in physics and chemistry, for example it can be used to predict or explain many of a molecule's properties, such as its dipole moment and its allowed spectroscopic transitions, without doing the exact rigorous calculations. To do this it is necessary to classify the states of the molecule using the irreducible representations from the character table of the symmetry group of the molecule. Among all the molecular symmetries, diatomic molecules show some distinct features and they are relatively easier to analyze.
Pelorism is the term, said to be first used by Charles Darwin, for the formation of 'peloric flowers' which botanically is the abnormal production of radially symmetrical (actinomorphic) flowers in a species that usually produces bilaterally symmetrical (zygomorphic) flowers. These flowers are spontaneous floral symmetry mutants. The term epanody is also applied to this phenomenon. Bilaterally symmetrical (zygomorphic) flowers are known to have evolved several times from radially symmetrical (actinomorphic) flowers, these changes being linked to increasing specialisation in pollinators.
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