symmetry of similarity;
radial symmetry
Reflection is the most well-known and most common form of symmetry found in nature. The mirror exactly reproduces what it "sees", but the order considered is reversed: your double's right hand will actually be left, since the fingers are placed on it in reverse order.
mirror symmetry
can be found everywhere: in the leaves and flowers of plants, architecture, ornaments. The human body, if we talk only about the external form, has a mirror symmetry, although not quite strict. Moreover, mirror symmetry is characteristic of the bodies of almost all living beings, and such a coincidence is by no means accidental.
Mirror symmetry has everything that can be divided into two mirror equal halves. Each of the halves serves as a mirror image of the other, and the plane separating them is called the plane of mirror reflection, or the mirror plane. This plane can be called an element of symmetry, and the corresponding operation can be called a symmetry operation.
rotational symmetry.
The appearance of the pattern will not change if it is rotated by some angle around the axis. The symmetry that arises in this case is called rotational symmetry. In many dances, the figures are based on rotational movements, often performed only in one direction (i.e. without reflection), for example, circle dances.
The leaves and flowers of many plants exhibit radial symmetry. This is such a symmetry in which a leaf or flower, turning around the axis of symmetry, passes into itself. On cross sections of the tissues that form the root or stem of a plant, radial symmetry is clearly visible. The inflorescences of many flowers also have radial symmetry.
Reflection at the center of symmetry.
An example of an object of the highest symmetry that characterizes this symmetry operation is a ball. Spherical shapes are widely distributed in nature. They are common in the atmosphere (fog drops, clouds), hydrosphere (various microorganisms), lithosphere and space. Spores and pollen of plants, drops of water released in a state of weightlessness on a spacecraft have a spherical shape. At the metagalactic level, the largest globular structures are globular galaxies. The denser the cluster of galaxies, the closer it is to a spherical shape. Star clusters are also globular shapes.
Translation, or the transfer of a figure over a distance.
Translation, or parallel transfer of a figure over a distance, is any unlimitedly repeating pattern. It can be one-dimensional, two-dimensional, three-dimensional. Translation in the same or opposite directions forms a one-dimensional pattern. Translation in two non-parallel directions forms a two-dimensional pattern. Parquet floors, wallpaper patterns, lace ribbons, paths paved with bricks or tiles, crystalline figures form patterns that have no natural boundaries.
Screw turns.
Translation can be combined with reflection or rotation, and new symmetry operations arise. Rotation by a certain number of degrees, accompanied by translation to a distance along the axis of rotation, generates helical symmetry - the symmetry of a spiral staircase. An example of helical symmetry is the arrangement of leaves on the stem of many plants.
The head of a sunflower has processes arranged in geometric spirals that unwind from the center outwards. The youngest members of the spiral are in the center.
In such systems, one can notice two families of spirals that unwind in opposite directions and intersect at angles close to right.
Following Goethe, who spoke of the striving of nature towards a spiral, it can be assumed that this movement is carried out along a logarithmic spiral, starting each time from a central, fixed point and combining translational movement (stretching) with a turn of rotation.
Similarity symmetry.
To the symmetry operations listed above, one can add the similarity symmetry operation, which is a kind of analogy of translations, reflections in planes, rotations around the axes, with the only difference that they are associated with a simultaneous increase or decrease in similar parts of the figure and the distances between them.
The symmetry of similarity, realized in space and time, manifests itself everywhere in nature on everything that grows. It is to the growing forms that countless figures of plants, animals and crystals belong. The shape of the tree trunk is conical, strongly elongated. Branches are usually arranged around the trunk in a helix. This is not a simple helix: it gradually narrows towards the top. And the branches themselves decrease as they approach the top of the tree. Therefore, here we are dealing with a helical axis of symmetry of similarity.
Living nature in all its manifestations reveals one and the same goal: every living object repeats itself in its own kind. The main task of life is Life, and the accessible form of being consists in the existence of separate integral organisms.
Radial-beam symmetry in nature.
Looking closely at the surrounding nature, you can see the common even in the most insignificant things and details. The shape of a tree leaf is not random: it is strictly regular. The leaf is, as it were, glued together from two more or less identical halves, one of which is mirrored relative to the other. The symmetry of the leaf is persistently repeated, whether it be a caterpillar, a butterfly, a bug, etc.
Flowers, mushrooms, trees, fountains have radial-beam symmetry. It can be noted here that on unpicked flowers and mushrooms, growing trees, a spouting fountain or a column of vapors, the symmetry planes are always oriented vertically.
Thus, it is possible to formulate in a somewhat simplified and schematized form a general law that is clearly and ubiquitously manifested in nature: everything that grows or moves vertically, i.e. up or down relative to the earth's surface, subject to radial-beam symmetry in the form of a fan of intersecting planes of symmetry. Everything that grows and moves horizontally or obliquely with respect to the earth's surface is subject to bilateral symmetry, leaf symmetry. Not only flowers, animals, lightly mobile liquids and gases, but also stones obey this universal law. This law affects the changing forms of clouds. On a calm day, they have a dome shape with more or less clearly expressed radial-radial symmetry.
Answers to the states (11)
11. Symmetry types of invertebrates
Symmetry, or the proportionality of the parts of the whole organism, is directly related to the nature of the adaptability of animals to the conditions of existence. Symmetry indirectly or directly reflects the features of the functional morphology, lifestyle and behavior of the animal.
Elements of symmetry necessary to determine the type of symmetry characteristic of a particular organism or group of organisms.
Center of symmetry is a point around which a body revolves. During rotation, the contours of the body continuously coincide when turning through any angle in any direction. Of living objects, a spherical egg with a nucleus located in the center can conditionally serve as an example. The colonial flagellate Volvox globator has a similar form, the body of which continuously rotates in the thickness of lake or pond water.
Axis of symmetry- This axis rotation. AT this case at animals, as rule is absent Centre symmetry. Then rotation maybe take place only around axes. At this axis more often Total It has of different quality poles. For example, at free-floating larvae coelenterates - gastrula on the one pole situated mouth, a on the opposite - sensitive aboral organ. At natural rotation around axes larva floats aboral body forward, a mouth back. At adults coelenterates, For example at hydra or anemones, on the one pole situated mouth, a on the friend - sole, which these motionless animals attached to substrate. Axis symmetry maybe coincide morphologically with anteroposterior axis body.
Plane of symmetry - This plane, passing through axis symmetry, coinciding with her and dissecting body on the two mirrored half. These half, located friend against friend, called antimers. For example, in a hydra, the plane of symmetry must pass through the mouth opening and through the sole. The antimeres of the opposite halves must have an equal number of tentacles located around the hydra's mouth. Hydra can have several planes of symmetry, the number of which will be a multiple of the number of tentacles. In anemones with a very large number of tentacles and gastric septa, many planes of symmetry can be drawn. In a jellyfish with four tentacles on a bell, the number of planes of symmetry will be limited to a multiple of four. Ctenophores have only two planes of symmetry - pharyngeal and tentacle. Finally, bilaterally symmetrical organisms have only one plane and only two mirror antimeres, respectively, the right and left sides of the animal.
Symmetry types V.N. Beklemisheva. Detailed analysis of symmetry elements and detailed classification of protist symmetry types:
Anaxon. The simplest with the most primitive architectonics (amoeba) are characterized by a complete lack of symmetry.
spherical(homaxonic). Symmetry with respect to rotations in three-dimensional space through arbitrary angles. There is a center of symmetry at which an infinite number of symmetry axes of an infinitely high order intersect. Characteristic of colonial radiolarians and coccidia.
Indefinitely polyaxonic(there is a center of symmetry and a finite, but indefinite number of axes and planes) - many sunflowers.
Correct polyaxon(a strictly defined number of symmetry axes of a certain order) - many radiolarians.
Stavraxon (monaxon) homopolar(there is one axis of symmetry with equal poles, that is, intersected in the center by a plane of symmetry, in which at least two additional axes of symmetry lie) - some radiolarians.
Monaxon heteropolar(there is one axis of symmetry with two unequal poles, the center of symmetry disappears) - many radiolarians and flagellates, testate rhizopods, gregarines, primitive ciliates.
Bilateral- diplomamonads, bodonids, foraminifers.
Symmetry of multicellular organisms.
Radial symmetry- a form of symmetry in which a body (or figure) coincides with itself when an object rotates around a certain point or line. Often this point coincides with the center of symmetry of the object, that is, the point at which an infinite number of axes or planes of bilateral symmetry intersect. In biology, one speaks of radial symmetry when one or more axes of symmetry pass through a three-dimensional being. Moreover, radially symmetrical animals may not have planes of symmetry. Usually two or more planes of symmetry pass through the axis of symmetry. These planes intersect in a straight line - the axis of symmetry. If the animal will rotate around this axis by a certain degree, then it will be displayed on itself (coincide with itself). As a rule, in multicellular animals, the two ends (poles) of a single axis of symmetry are not equivalent (for example, in jellyfish, the mouth is on one pole (oral), and the top of the bell is on the opposite (aboral). Such symmetry (a variant of radial symmetry) in comparative anatomy is called uniaxial-heteropoly.In a two-dimensional projection, radial symmetry can be preserved if the axis of symmetry is directed perpendicular to the projection plane.In other words, the preservation of radial symmetry depends on the viewing angle.Radial symmetry is characteristic of many cnidarians, as well as most echinoderms.Among them is the so-called pentasymmetry based on five planes of symmetry.In echinoderms, radial symmetry is secondary: their larvae are bilaterally symmetrical, and in adult animals, external radial symmetry is violated by the presence of a madrepore plate.
Bilateral symmetry(bilateral symmetry) - symmetry of mirror reflection, in which the object has one plane of symmetry, with respect to which its two halves are mirror symmetrical. In animals, the appearance of bilateral symmetry in evolution is associated with crawling along the substrate (along the bottom of the reservoir), in connection with which the dorsal and ventral, as well as the right and left halves of the body appear. In general, among animals, bilateral symmetry is more pronounced in actively mobile forms than in sessile ones. Bilateral symmetry is characteristic of all sufficiently highly organized animals, except for echinoderms.
Rotational-translational symmetry. This type of symmetry has a limited distribution in the animal kingdom. This symmetry is characterized by the fact that when turning through a certain angle, a part of the body protrudes slightly forward and its dimensions are increased logarithmically by a certain amount with each subsequent step. Thus, there is a combination of acts of rotation and translational motion. An example is the spiral chambered shells of foraminifera (single-celled), as well as the spiral chambered shells of some cephalopods (modern nautilus or fossil ammonite shells). With some condition, non-chambered spiral shells of gastropod mollusks can also be included in this group.
What is ray symmetry?
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- Multicellular animals form the largest group of living organisms on the planet, numbering more than 1.5 million species. Leading their origin from the simplest, they have undergone significant transformations in the process of evolution associated with the complication of organization.
One of the most important features of the organization of multicellular organisms is the morphological and functional difference between the cells of their body. Over the course of evolution, similar cells in the body of multicellular animals specialized in performing certain functions, which led to the formation of tissues.
Different tissues united into organs, and organs into systems of organs. To implement the relationship between them and coordinate their work, the nervous and endocrine regulatory systems were formed. Thanks to the nervous and humoral regulation of the activity of all systems, a multicellular organism functions as an integral biological system.
The prosperity of a group of multicellular animals is associated with the complication of the anatomical structure and physiological functions. Thus, an increase in body size led to the development of the alimentary canal, which allowed them to eat large food material, which supplies a large amount of energy for the implementation of all life processes. The developed muscular and skeletal systems ensured the movement of organisms, the maintenance of a certain body shape, protection and support for organs. The ability to actively move allowed animals to search for food, find shelter and settle.
With an increase in the size of the body of animals, a need arose for the appearance of intratransport circulatory systems that deliver nutrients, oxygen, and remove end products of metabolism to tissues and organs remote from the surface of the body.
The liquid tissue blood has become such a circulatory transport system.
The intensification of respiratory activity went in parallel with the progressive development of the nervous system and sensory organs. The central sections of the nervous system moved to the anterior end of the animal's body, as a result of which the head section became isolated. Such a structure of the anterior part of the animal's body allowed it to receive information about changes in the environment and adequately respond to them.
According to the presence or absence of an internal skeleton, animals are divided into two groups: invertebrates (all types except Chordates) and vertebrates (Chordates).
Depending on the origin of the mouth opening in an adult organism, two groups of animals are distinguished: primary and secondary-stomes. Protostomes unite animals in which the primary mouth of the embryo at the gastrula blastopore stage remains the mouth of an adult organism. These include animals of all types except echinoderms and chordates. In the latter, the primary mouth of the embryo turns into an anus, and the true mouth is formed a second time in the form of an ectodermal pocket. For this reason, they are called deuterostomes.
According to the type of symmetry of the body, a group of radiant, or radially symmetrical, animals (types of Sponge, Coelenterates and Echinoderms) and a group of bilaterally symmetrical (all other types of animals) are distinguished. Radial symmetry is formed under the influence of the sedentary lifestyle of animals, in which the entire organism is placed in relation to environmental factors in exactly the same conditions. These conditions form the arrangement of identical organs around the main axis passing through the mouth to the attached pole opposite to it.
Bilaterally symmetrical animals are mobile, have one plane of symmetry, on both sides of which there are various paired organs. They distinguish between left and right, dorsal and ventral sides, anterior and posterior ends of the body.
Multicellular animals are extremely diverse in structure, life characteristics, different in size, body weight, etc. Based on the most significant common structural features, they are divided into 14 types, some of which are discussed in this manual. - Radial (radial) symmetry is a form of symmetry in which a body (or figure) coincides with itself when an object rotates around a certain point or line.
As a rule, in multicellular animals, the two ends (poles) of a single axis of symmetry are not equivalent (for example, in jellyfish, the mouth is on one pole (oral), and the top of the bell is on the opposite (aboral). Such symmetry (a variant of radial symmetry) in comparative anatomy is called In a 2D projection, radial symmetry can be preserved if the axis of symmetry is directed perpendicular to the projection plane.In other words, the preservation of radial symmetry depends on the viewing angle.
Radial symmetry is characteristic mainly for intestinal animals. Intestinal cavities, both sessile and pelagic (jellyfish), are characterized by radial-axial symmetry, in which similar parts are located around the axis of rotation, and this symmetry can be of a very different order, depending on what angle the animal's body should be rotated in order to create a new position is the same as the original. Thus, 4-, 6-, 8-beam symmetry and more can be obtained, up to symmetry of the order of infinity. Radiolarians have radial-axial symmetry with the same poles, or, as they say, homopolar. Coelenterates have heteropolar axial symmetry: one pole of symmetry carries the mouth and tentacles (oral), the other (aboral) serves for attachment (polyp stage), or in floating forms it carries the sense organ (ctenophores), or not armed with anything (jellyfish).
In some jellyfish, a stalk is formed on this aboral side for attachment to underwater objects (Lucernariida). Violation of radial-axial symmetry occurs with a decrease in the number of tentacles or a change in the shape of the oral fissure, esophagus, and branches of the digestive system. The number of tentacles can decrease to one (Mopobrachium), and then their radial arrangement is replaced by a two-sided one. The pharynx can be flattened, and then two-sided symmetry is also obtained, this is also facilitated by the formation of siphonoglyphs in the pharynx (groove along the pharynx).
The greatest complication of radial-axial symmetry is observed in ktenophores, where, in addition to 8-beam symmetry, 4-beam and two-sided symmetry is observed in the arrangement of individual parts of the body and organs. This is a very significant point, since most zoologists derive both trunks of higher animals, both primary and deuterostomes, from ctenophore-like ancestors.
The heteropolar radial-axial symmetry is quite consistent with the way of life of the coelenterates of a fixed existence in an attached position or slow swimming with the help of jet propulsion.
On the other hand, from the complex type of radial-axial symmetry of the ctenophore, one can pass to bilateral symmetry, or, as they say, the symmetry of a mirror image, the only plan of symmetry of three-layered animals, the symmetry of rapid movement, with the development of the anterior end of the body along the movement, with a central brain cluster and main sense organs, dorsal and abdominal, right and left sides of the body.
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Ryzhov Ilya
In the course of implementation, he established the mathematical connection of natural phenomena, found out that it is much more pleasant for the human eye to look at symmetrical things. After conducting a study of various sources of information about symmetry, I came to the conclusion that nature is arranged in accordance with the laws of symmetry. All living things in nature have the property of symmetry. Symmetry can be seen among the flowers and on the leaves of the trees. The property of symmetry, inherent in living nature, was used by man in his achievements: he invented the airplane, created unique buildings of architecture. Yes, and the man himself is a symmetrical figure
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I would like to present to your attention my design and research work on the topic "Symmetry in wildlife" (slide No. 1)
The purpose of my work:Show the connection between symmetry and nature, consider what types of symmetry are found in the animal and plant world. (slide number 2) Tasks: Give an idea of \u200b\u200bsymmetry in nature; through the concept of "symmetry" to reveal the most important connections between the phenomena of symmetry and living nature; prove that we are indeed surrounded by symmetrical objects; show the significant role of symmetry in wildlife (slide No. 3) To solve the tasks, I conducted my own research, having studied material from the media, the Internet, special literature, analyzing the appearance of insects, plants, birds, animals, humans. Nominated hypothesis : Is symmetry really found in wildlife and what role does it play? (slide number 4)
Subject of study(slide number 5)
Symmetry as a rule.
Object of study
Definition of the concept and types of symmetry, symmetry and its role in the life of plants, animals and humans.
Project relevancedue to the fact that symmetry surrounds a person, finding its manifestation both in living and inanimate nature. The explanation of the laws of symmetry is important for understanding beauty, harmony, and life. The results of the project will be of interest to students of secondary and primary schools. (slide number 6)
There are a large number of definitions of the concept of "symmetry", but I chose this one. (slide number 7)
SYMMETRY - proportionality, proportionality, uniformity in the arrangement of parts
What role does symmetry play in the environment? (slide number 8)
Symmetry pleases the eye and inspires poets, allows living organisms to better adapt to their environment and simply survive.
In mathematics, various types of symmetry are considered.
Types of symmetry (slide number 9)
a) Bilateral (bilateral) axial symmetry
(lat. bi - two, two, lateralis - lateral).
b)Beam symmetry(= radiant, radial)
in) Central symmetry
G) Mirror symmetry
Nature is an amazing creator and master. All living things in nature have the property of symmetry. (slide No. 10,11)
The symmetry characteristic of representatives of the animal world is called bilateral symmetry.
If you look at any insect from above and mentally draw a straight line (plane) in the middle, then the left and right halves of the insects will be the same in location, size, and color. After all, we have never seen that in a beetle or dragonfly, in any other insect, the paws on the left would be closer to the head than on the right, and the right wing of a butterfly or ladybug would be larger than the left. This does not happen in nature, otherwise insects would not be able to fly.
Bilateral symmetry is characteristic of most multicellular animals and arose in connection with active movement. Insects and some plants also have bilateral symmetry. For example, (slide number 12) the shape of the leaf is not random, it is strictly natural. It is, as it were, glued together from two more or less identical halves. One of these halves is mirrored with respect to the other. Botanists call this symmetry bilateral or twice lateral. But not only a tree leaf has such symmetry. Mentally, you can cut an ordinary caterpillar into two mirror equal parts. A beautiful butterfly with bright colors swept past. It also consists of two identical halves. Even the spotted pattern on her wings obeys this geometry. And a bug peeping out of the grass and a midge flashing by, a plucked branch - everything obeys the symmetry of the leaf. Everything that grows and moves horizontally or obliquely with respect to the earth's surface is subject to bilateral symmetry, i.e. axial. The same symmetry is preserved in organisms that have gained the ability to move. Albeit without a specific direction. These creatures include starfish and urchins.
The human body is built on the principle of bilateral symmetry. (slide number 13) Most of us consider the brain as a single structure, in reality it is divided into two halves. These two parts - two hemispheres - fit snugly together. The left hemisphere controls the right side of the brain, while the right hemisphere controls the left side. The physical symmetry of the body and brain does not mean that the right side and the left side are equal in all respects. It is enough to pay attention to the actions of our hands to see the initial signs of functional symmetry.
Our own mirror symmetry is very convenient for us, it allows us to move in a straight line and turn right and left with equal ease.Everything that grows and moves horizontally or obliquely with respect to the earth's surface is subject to bilateral symmetry.
Another kind of symmetry: (slide 14.15)
Radial or radial (in mathematical language, this symmetry is called rotational symmetry)
Radiation symmetry is typical, as a rule, for animals leading an attached lifestyle. Hydra is one of these animals. If an axis is drawn along the body of the hydra, then its tentacles will diverge from this axis in all directions, like rays. If we consider the petals of chamomile, we can see that they also have a plane of symmetry. Thus, we can conclude that everything that grows or moves vertically down or up relative to the earth's surface is subject to radial-beam symmetry.
From everything studied, it is possible to formulate a general law that is clearly and everywhere manifested in nature. Everything that grows or moves vertically, that is, up or down relative to the earth's surface, is subject to ray symmetry. Interestingly, the human eye also has radial symmetry. (slide No. 16) The next type of symmetry is central (slide No. 17)
There is no concept of a center of symmetry in Euclid's Elements, however, in the 38th sentence of the XI book, the concept of a spatial axis of symmetry is contained. The concept of a center of symmetry was first encountered in the 16th century.
Another type of symmetry - mirror (slide number 18)
Mirror symmetrywell known to every person from everyday observation. As the name itself shows, mirror symmetry connects any object and its reflection in a flat mirror. One figure (or body) is said to be mirror symmetrical to another if together they form a mirror symmetrical figure (or body). It is important to note that two bodies that are symmetrical to each other cannot be nested or superimposed on each other. So the glove of the right hand cannot be put on the left hand. Symmetrically mirrored figures, for all their similarities, differ significantly from each other. To verify this, it is enough to bring a sheet of paper to a mirror and try to read a few words printed on it, the letters and words will simply be turned right to left. For this reason, symmetrical objects cannot be called equal, so they are called mirror equal. I have carried out research work, the purpose of which is to find out the reasons for the symmetry in the plant kingdom. I placed bean sprouts in two transparent tubes. One tube was placed in a horizontal position, and the other in a vertical position. A week later, I found that as soon as the root and stem grew beyond the horizontal tube, the root began to grow straight down, and the stem up. I believe that the downward growth of the root is due to gravity; upward growth of the stem - by the influence of light. Experiments carried out by cosmonauts aboard the orbital station under weightless conditions showed that in the absence of gravity, the habitual spatial orientation of seedlings is disturbed. Therefore, under the conditions of gravity, the presence of symmetry allows plants to take a stable position. Studying popular science literature, in order to identify symmetry in some of the studied plants and animals, I received: (slide No. 20)
This research topic helps to understand the relationship of mathematics with biology and with the outside world. (slide number 21) I established the mathematical connection of natural phenomena, found out that it is much more pleasant for the human eye to look at symmetrical things. After researching various sources of information about symmetry, I came to the conclusion that nature is arranged in accordance with the laws of symmetry. All living things in nature have the property of symmetry. Symmetry can be seen among the flowers and on the leaves of the trees. The property of symmetry, inherent in living nature, was used by man in his achievements: he invented the airplane, created unique buildings of architecture. Yes, and the man himself is a symmetrical figure.Therefore, symmetry did not arise by chance - perhaps symmetrical objects are easier for living beings to perceive.
While working on the project, I touched the mysterious mathematical beauty. Mathematics is a language, the language of nature. Without knowing the language, you cannot understand the beauty of the world around you.
To the question What is ray symmetry? given by the author Katya Chernykh the best answer is Radial (radial) symmetry is a form of symmetry in which a body (or figure) coincides with itself when an object rotates around a certain point or line.
As a rule, in multicellular animals, the two ends (poles) of a single axis of symmetry are not equivalent (for example, in jellyfish, the mouth is on one pole (oral), and the top of the bell is on the opposite (aboral). Such symmetry (a variant of radial symmetry) in comparative anatomy is called In a 2D projection, radial symmetry can be preserved if the axis of symmetry is directed perpendicular to the projection plane.In other words, the preservation of radial symmetry depends on the viewing angle.
Radial symmetry is characteristic mainly for intestinal animals. Intestinal cavities, both sessile and pelagic (jellyfish), are characterized by radial-axial symmetry, in which similar parts are located around the axis of rotation, and this symmetry can be of a very different order, depending on what angle the animal's body should be rotated in order to create a new position is the same as the original. Thus, 4-, 6-, 8-beam symmetry and more can be obtained, up to symmetry of the order of infinity. Radiolarians have radial-axial symmetry with the same poles, or, as they say, homopolar. In coelenterates - heteropolar axial symmetry: one pole of symmetry carries the mouth and tentacles (oral), the other (aboral) serves for attachment (polyp stage), or in floating forms it carries the sense organ (ctenophores), or not armed with anything (jellyfish).
In some jellyfish, a stalk is formed on this aboral side for attachment to underwater objects (Lucernariida). Violation of radial-axial symmetry occurs with a decrease in the number of tentacles or a change in the shape of the oral fissure, esophagus, and branches of the digestive system. The number of tentacles can decrease to one (Mopobrachium), and then their radial arrangement is replaced by a two-sided one. The pharynx can be flattened, and then two-sided symmetry is also obtained, this is also facilitated by the formation of siphonoglyphs in the pharynx (groove along the pharynx).
The greatest complication of radial-axial symmetry is observed in ktenophores, where, in addition to 8-beam symmetry, 4-beam and two-sided symmetry is observed in the arrangement of individual parts of the body and organs. This is a very significant point, since most zoologists derive both trunks of higher animals, both primary and deuterostomes, from ctenophore-like ancestors.
The heteropolar radial-axial symmetry is quite consistent with the way of life of the coelenterates - a motionless existence in an attached position or slow swimming with the help of jet propulsion.
On the other hand, from the complex type of radial-axial symmetry of the ctenophore, one can pass to bilateral symmetry, or, as they say, the symmetry of a mirror image, the only plan of symmetry of three-layered animals, the symmetry of rapid movement, with the development of the anterior end of the body along the movement, with a central brain cluster and main sense organs, dorsal and abdominal, right and left sides of the body.
..more details - . berl. ru/article/ nauka/cimmetria_u_givotnyh.htm here (remove pro)