WO2013097872A1 - Three-dimensional systems structured by nesting six polyhedra respectively in a sphere - Google Patents

Abstract

The invention relates to three-dimensional systems structured by nesting six polyhedra respectively in a sphere, each of said systems being formed by four assemblies having a regular polyhedral configuration (C1, C3, C4, C5), one assembly having a regular star polyhedral shape (C2) and one assembly having a spherical shape (C6), which are housed inside one another without leaving any empty inner spaces, such that they are enclosed in the sixth assembly which has a spherical external form that is different from the previous assemblies, each assembly of each system being made up of a predetermined number of parts in accordance with the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13), the parts thereof being assembled together magnetically by means of several internal magnets which are positioned in a pre-determined ordered manner inside each part and which are also used to house same inside the immediately larger assembly, in the form a jigsaw with successive levels of difficulty. Figure 1 is a perspective view of an illustrative section of the systems.

Description

 DESCRIPTION

 Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively.

 It refers to the invention according to the title thereof, to transformable devices, composed or integrated by magnetic assembly parts, which allows different independent assemblies of different sizes, but proportional to each other, to be built to admit the respective housing of one another and their once in a few general sets.

 The culmination of each of the systems, according to the invention, requires certain difficulty coefficients for the construction of the different independent sets of each system and these entail increasing levels of difficulty for the integration of said sets into each other and that of these in each general set.

 The development of this invention is aimed at manufacturing them in recycled plastic A.B.S. or in a vegetable plastic based on rice, or other types of plastic, metals, wood, among others.

 Background of the invention

 Conducting an investigation of the prior art, we find the following documents: WO2011143828, piece of the puzzle that is easy to be folded and folded are protected, including two pieces of the unit puzzle (1, 2) connected together. The puzzle pieces of the unit (1, 2) are connected by their outer sides by means of a sheet (3) with a certain width. The inner part of the connection position of the two pieces of the puzzle of the unit (1, 2) with groove shapes, and the outer part is flat. With the previous structure, folded and folded of the pieces of the unit puzzle (1, 2) a benefit can be imparted, so the manufacturing precision does not have to be very exact.

The form of assembly of the different members or parts that make up both the independent assemblies and the general assembly, by means of several internal magnets strategically placed in each piece, make the conception of this invention with the very different and diverse assembly systems that in different assembly less assimilable. These types of sets exist in the prior art or prior art. We could summarize that, with these or similar characteristics, it is not possible to find other construction assemblies that are assembled and joined piece by piece.

 In the true and primitive construction systems called mecanos, the perforated structure of the pieces allowed their union by means of screws, nuts, bolts or the like.

 With the development of these structures in plastic materials, it has been possible to develop joint assemblies similar to the previous ones and others by means of the tongue and groove assembly of geometric protrusions that fit into respective housings with symmetrical configuration.

 Other clamping assembly systems have also been developed so that a female member in the form of a fork or in an equivalent form receives a complementary male member adjustable to pressure in said housing, even with the possibility of articulating, or turning, or Both functions

 Inventive activity

 The devices develop independent sets, specific, precise and with a certain regular geometric configuration.

 A certain configuration and proportional volumes that allow to register or to lodge in each other in respective and logical proportion to their sizes.

 Independent assemblies that integrated respectively into each other, are finally housed in a general set that has a geometric, external development, totally different from the internal assemblies, offering a solid spherical exterior appearance.

 Independent sets consisting of groups of pieces that follow a mathematical sequence called Fibonacci (1, 1, 2,3,5,8,13), and with a size proportional to the scale of the number of gold Fi (1,618), which at to solve these systems, solid figures in the form of spheres are achieved.

A general system internally adapted to accommodate the rest of integrated independent assemblies; composed of a minimum of pieces that are within the Fibonacci sequence and with solid spherical exterior appearance. Description of the invention

 The devices are constituted, according to some of their characteristics, by a group of four sets of regular polyhedral general configuration, a set of regular crashed polyhedral configuration, and a set of spherical configuration giving a total of six sets of internal geometric general regular configuration emptied internally so that the internal emptying of said independent assemblies constitutes the housing for the independent assembly immediately lower in volume since such assemblies are proportionally complementary in progressive increase from the first to the sixth.

 Another characteristic of said independent assemblies, according to the invention, is that they are formed by a certain number of pieces that follow the Fibonacci sequence (1, 1, 2,3,5,8,13) and that are joined by magnetic means which constitutes the means to assemble each independent set and the means to fit the assemblies into each other.

 Another feature of the devices, is that the assembly of the said independent sets, are carried out in a precise and mathematical order, being impossible to place them in another way and, consequently, the assembly between independent sets, require a certain level of difficulty that hardens in order proportional to the solution of the system, which culminates with the accommodation in a general set.

 A general assembly according to the devices whose main characteristic is to present an external volume of solid uniform appearance and of a geometric configuration different from the internal assemblies so that, the envelope assembly composed of several pieces according to the Fibonacci sequence (1, 1, 2,3 , 5,8,13) give rise to thousands of possibilities, but only one is correct due to the strategic location of the internal magnets of the pieces.

All these interpretations according to the invention give two options to the devices, that of being able to be made starting from the assembled or fully awakened assembly or starting from intermediate situations, with the independent assemblies assembled, semi-assembled, semi-assembled, so that the user acquires gradual knowledge of each system that in turn increases the degree of difficulty as the number of pieces increases sequentially in each system. Each system has a certain number of pieces that follow the Fibonacci sequence (1, 1, 2,3,5,8,13), and that system is composed of independent groups that are in turn composed of a number of pieces that also follow a Fibonacci sequence

(1, 1, 2,3,5,8,13), giving rise to the first 33-piece system that is the result of the sum of the first seven numbers of the sequence (1, 1, 2,3,5, 8.13), or the 54-piece system that is the result of the sum of the first eight numbers of the sequence (1, 1, 2,3,5,8,13,21), or the 143-piece system which is the result of the sum of the first ten numbers of the sequence (1, 1, 2,3,5,8,13,21, 34,55), etc.

 Each system is composed of six independent sets, the same ones that in turn are composed of a defined number of pieces that follow a Fibonacci sequence (1, 1, 2,3,5,8,13), and which can also be assembled by separated.

 Each system is structurally based on the nesting of the strategic sectioning of the five regular polyhedra, and a tetrahedral star in a sphere without leaving internal empty spaces, resulting in a solid-looking sphere.

 Each independent set of each system is based on the strategic sectioning of the five regular polyhedra, the regular crashed polyhedron (tetrahedral star), and the sphere.

 The philosophy with which this three-dimensional system is designed is based on techno scientific, playful, and historical aspects of the creation of the universe such as the Big Bang, the Fibonacci sequence (1, 1, 2,3,5,8,13 ) clearly explained in the previous paragraphs, the constant Fi (1, 618) since the systems are built on this scale, the theory of the elements (fire, earth, air, water, ether) represented by the five regular polyhedra according to Plato , and according to several psychologists affirm that when interacting with these regular volumes, the human being jointly coordinates the two cerebral hemispheres, increasing the logical and creative capacities in the human being, own capacities offered by each cerebral hemisphere.

As an example for this description, as well as for the rest of this documentation, we will take as a guide the three-dimensional system of 33 pieces, in which its first independent set and of smaller volume, according to the device, is an octahedron, that is to say a polyhedron regular of eight triangular faces, with one of them emptied in which another regular polyhedron of four triangular faces called tetrahedron but with three quarters less than the volume of the octahedron.

 This first independent set, according to the invention, consists of two pieces that are joined by the action of the internal magnets in each piece, and when the tetrahedron is housed inside the octahedron the first independent set is assembled with minimal difficulty, being ready to stay In the second set.

 The second set according to the invention, has a configuration analogous to that of the first set but with a starry outer shape and with an octahedral void, it is a star octahedron known as a tetrahedral star. It is composed of a set of two pieces following the Fibonacci sequence (1, 1, 2,3,5,8,13), axially symmetrical, each consisting of four tetrahedra joined in such a way that they leave a pyramid-shaped emptying with quadrangular base, that when joining the two pieces by the square sides, there is an internal emptying that houses the first set millimetrically.

 The coupling of these two sets implies a certain level of difficulty due to the strategic location of the internal magnets in the respective pieces.

 The third set according to the invention is also constituted by a regular six-sided polyhedron called a hexahedron or cube with an internal emptying in the shape of a tetrahedral star. This set is composed of three pieces, following the Fibonacci sequence (1, 1, 2,3,5,8,13), of varied geometry, each joined by two square faces respectively in which semiregular tetrahedra with equal faces are glued in pairs. Each of these pieces have three, four and five semiregular tetrahedra attached to their inner faces, respectively, joined by their edges of equal magnitude as the edges of the tetrahedral star of the second set, and aligned parallel to the edges of the squares with the only longer edges of the semiregular tetrahedra.

 The internal emptying of this third set is exactly calculated and designed to accommodate the second set, also with a certain difficulty coefficient due to the shape of its pieces and the location of the magnets inside them.

The fourth set, according to the invention, is an externally polyhedral set of twelve pentagonal faces, of compact appearance, with a Hexahedral interior emptying, perfectly adapted and calculated for the accommodation of the third set with its respective difficulty.

 The previous set according to the invention consists of five pieces following the Fibonacci sequence (1, 1, 2,3,5,8,13), of varied shape and geometry, product of the strategic sectioning of the regular polyhedron called dodecahedron, with an internal emptying hexahedral, which are joined by the attraction effect of the internal magnets in each piece.

 The fifth set, according to the invention, is also an externally polyhedral set of twenty triangular faces, of a compact appearance, with a dodecahedral interior emptying, perfectly adapted and calculated for the accommodation of the fourth set with a degree of difficulty more than the previous set. This set according to the invention consists of eight pieces following the Fibonacci sequence (1, 1, 2,3,5,8,13), of varied shape and geometry, product of the strategic sectioning of the regular polyhedron called icosahedron, with a dodecahedral interior emptying , which are joined by the attraction of the internal magnets of each piece.

 The sixth and final set, according to the invention, is an externally spherical assembly, of compact appearance, with an internal icosahedral void, perfectly adapted and calculated for the accommodation of the fifth set with the highest level of difficulty.

 This last set, according to the invention, consists of thirteen pieces of varied shape and geometry with the appearance of regular spherical-triangular caps, product of the strategic sectioning of the sphere with an internal dodecahedral emptying, which are joined by the attraction of internal magnets of his pieces.

 Succinctly these are the characteristics of the different sets that make up the composition of the three-dimensional system of 33 pieces that, like this system, the other systems are developed following these characteristics with the difference that each independent set of each system is composed of a well defined number of pieces, as the case may be, and that said independent sets can be assembled and lodged successively within each other in a process that entails eleven levels of difficulty respectively.

A broader idea of the characteristics of the invention will be carried out below, when referring to the sheets of the drawings that are attached here, somewhat schematic and only by way of example, representing the preferred and vital details of the 33-piece system, which is the pattern with which these three-dimensional systems are designed.

 In the drawings:

 Figure 1 is a perspective view of the illustrative section of three-dimensional systems.

 Figure 2 is a perspective view of the first armed assembly.

Figure 3 is a view of the first set with its parts disassembled.

 Figure 4 is a perspective view of the second armed assembly.

 Figure 5 is a view of the second set with its parts removed, and with the first set assembled to the assembly center.

 Figure 6 is a perspective view of the third armed assembly.

Figure 7 is a view of the third set with its parts removed, and with the second set assembled to the assembly center.

Figure 8 is a perspective view of the fourth armed assembly, and with the third armed assembly, to the assembly center.

 Figure 9 is a view of the fourth set with its parts disassembled

 Figure 10 is a perspective view of the fifth armed assembly, and with the fourth armed assembly, to the assembly center.

 Figure 11 is a view of the fifth set with its parts disassembled.

 Figure 12 is a perspective view of the sixth and final armed set.

 Figure 13 is a view of the two representative pieces of the sixth set as well as the fifth set assembled, to the assembly center.

 Preferred embodiment of the invention

Aspects of the preferred embodiment of the invention, outlined in the different drawing figures previously developed comprise the six main sets that integrate each of the three-dimensional systems, and which according to these illustrations are indicated in order to their respective volumes with (C1) the first set, with (C2) the second set, with (C3) the third set, with (C4) the fourth set, with (C5) the fifth set, all of them with polyhedral outer development and empty interior; being (C6) the sixth and final set that has spherical exterior and interior icosahedral emptying.

 According to the 33-piece system, the smaller assembly (C1) consists of two pieces as shown in Figure 2. It comprises two pieces; the tetrahedron (13) and the octahedron (14), with internal emptying (15) in the form of a tetrahedron that allows the perfect assembly of the piece (13) inside the piece (14) by effect of the internal magnets (+/- ), strategically located in its parts, to achieve a single resolution of its assembly.

 According to the 33-piece system, said set (C2) is also composed of two symmetrical pieces (21) with a quadrangular base (22) and four starry faces formed by tetrahedra (23). These pieces have a pyramidal emptying with a square base (24) in which half of the octahedron (14) is housed, the same occurs with the other symmetrical piece (21) leaving an internal emptying in the form of an octahedron when said symmetrical pieces are joined ( 21) by joining the sides of its square base (24) giving rise to the space occupied by the assembly (C1) by the effect of the magnets (+/-) strategically located in their respective pieces to obtain a single form of resolution.

 According to the 33-piece system, the referred set (C3), with a polyhedral structure as well as the previous ones, consists of three pieces (31, 32, 33) which are the product of the strategic sectioning of the hexahedron or cube with an internal emptying in the form of a tetrahedral star, which allows the exact accommodation of the set (C2).

The piece (31) is composed of two squares (311, 312) that are joined perpendicularly by their respective edges, and that on the inner side at the 90 degree angle, a semiregular tetrahedron with equal sides two by two is attached ( 313), the same one that joins by its major edge according to the graph of the piece (31), also on the inner side of the square (312), two semi-regular tetrahedra with equal sides two by two (313) are glued together, aligned with their edges greater than the edges of the square (312) according to the graphic of the piece (31). The same happens with the pieces (32 and 33), with the difference that the piece (32) has on its inner faces (314, 315), glued four semiregular tetrahedra of equal sides two by two according to the graphic of the piece (32), and the piece (33), has glued on its inner faces (316, 317) five semiregular tetrahedra of equal sides two by two (313), as shown in the piece (33).

 When solving said assembly (C3), it leaves an internal emptying in the form of a tetrahedral star with the exact volume of the assembly (C2) to accommodate this millimeter, thanks to the internal magnets (+/-) strategically located to obtain a single form of armed, and thus advance in the degree of difficulty of the puzzle.

 According to the 33-piece system, the referred set (C4), with external dodecahedron structure, and following the Fibonacci sequence (1, 1, 2,3,5) consists of five pieces volumetrically reported (41, 42, 43, 44 , 45), which are the product of a strategic sectioning of the dodecahedron with an internal emptying in the form of an exaggeration, which allows the exact accommodation of the assembly (C3).

 The pieces (42, and 43), are volumetric and structurally identical, but different in the magnetic aspect, due to the polarity of their internal magnets (+/-), these pieces have a pyramidal emptying of triangular base (421). The piece (41) has a report volume with a pentagonal face (41) of exact area to the face of the dodecahedron (C4), and the pieces (44, and 45) are similar but not equal pieces, which together form the space to accommodate the piece (41), these two pieces (44, and 45), have pyramidal dumps with a triangular base (421), identical to the dumps of the pieces (42, and 43).

 When solving said assembly (C4), by action of the internal magnets (+/-) strategically located inside said pieces, it gives rise to the internal space or emptying in the form of a cube, allowing the millimeter housing of the assembly (C3), aspect which gives a greater degree of difficulty to the present puzzle.

According to the 33-piece system, the referred set (C5), with an external appearance equal to the icosahedron, and following the Fibonacci sequence (1, 1, 2,3,5,8), is made up of eight pieces (51, 52, 53,54,55,56,57,58), of volume and structure report, product of the strategic sectioning of the icosahedron with an internal emptying in the form of dodecahedron, which allows the millimeter housing of the set (C4). The pieces (51, 52.53, and 54), are volumetric and structurally identical, but different in the magnetic aspect due to the polarity of their internal magnets (+/-). The pieces (55, and 56), are also volumetric and structurally identical, but different in the magnetic aspect due to the polarity of their internal magnets (+/-). And the remaining pieces (57, and 58), are also identical between them, but not in the magnetic aspect due to the polarity of their internal magnets (+/-).

 The group of pieces (51, 52,53,54) are axially symmetrical with the group of pieces (55, and 56), that is, some are the reflection of the others, of course, only in the volumetric and structural aspect, since in the magnetic aspect, all are different.

 When solving the group (C5), an icosahedron is formed with an internal recess capable of accommodating the whole millimeter (C4), creating a more difficult degree to the puzzle, since of several possibilities, there is only one way of assembling the location strategic of the internal standards of its pieces.

 According to the 33-piece system, the final envelope or assembly (C6) has a general spherical external shape. It consists of thirteen pieces following the Fibonacci sequence (1, 1, 2,3,5,8,13). These thirteen pieces are divided into two groups of seven (61) and six (62) pieces respectively. The seven pieces (61) are identical in volume and structure, but different in the magnetic aspect (+/-), they have a rhomboid spherical cap shape consisting of two equilateral triangular volumes (62) glued by their bases. The other six pieces (62), are also identical to each other in the aspects of volume and structure, but not in the magnetic aspect (+/-), they are shaped like triangular caps with equal edges.

When solving the assembly (C6), a sphere of compact appearance is formed with an internal recess in the form of icosahedron that allows the millimeter housing of the assembly (C5). Its solution depends on the correct and unique form of assembly, due to the strategic location of the internal magnets (+/-) of its pieces, since it has more than three thousand possibilities due to the number of pieces that make up the assembly (C6) , and by the number of pieces of the group (C5) that is in the immediately lower position, and, taking into account the arrangement of the internal magnets in those pieces, the possibilities grow to more than a million and a half, achieving this forms a high ceiling of difficulty in the assembly of the puzzle. The assembly of these six sets is carried out with coefficients of certain difficulty that are called difficulty levels, and comprise up to eleven levels in which the difficulty varies according to the sequence given in the assembly.

 As an example, levels can be developed as follows:

 FIRST LEVEL: It is done with the two pieces of the first set.

 SECOND LEVEL: It is done with the two pieces of the second set.

THIRD LEVEL: It is done with the assembly of the three pieces of the third set.

 FOURTH LEVEL: It is done with the assembly of the five pieces of the fourth set.

 FIFTH LEVEL: It is done with the assembly of the eight pieces of the fifth set.

 SIXTH LEVEL: It is done with the assembly of the thirteen pieces of the sixth set.

 SEVENTH LEVEL: It is done with the combination of the two pieces of the first set and the two pieces of the second set, transforming it into a single set.

 EIGHTH LEVEL: It is done by combining the two pieces of the first set, the two pieces of the second set and the three pieces of the third set, transforming it into a single set.

 NINTH LEVEL: It is done by combining the two pieces of the first set, two of the second, three of the third, and five of the fourth set, transforming it into a single set.

 TENTH LEVEL: It is done by combining the two pieces of the first set, the two of the second, the three of the third, the five of the fourth, and the eight pieces of the fifth set, transforming it into a single set.

ELEVENTH LEVEL: It is done by combining all the pieces of the puzzle, including the thirteen pieces of the set (C6), following a logical order that allows to advance in ascending form according to the Fibonacci sequence (1, 1, 2,3,5,8, 13) until reaching the sphere, transforming into a single compact spherical set, without spaces internal voids, and that said sphere houses the five Platonic solids and a tetrahedral star, fundamental aspects of this and all possible three-dimensional systems that follow the Fibonacci sequence, fitting with the characteristics of this invention.

 Once the nature of the invention has been conveniently described, it is stated for the appropriate purposes that it is not limited to the exact details of this presentation, but on the contrary, it will introduce the modifications deemed appropriate, of course, without altering the essential characteristics thereof, which are claimed below.

Claims

1 CLAIMS Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively.  1. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, consisting of groups of independent assemblies composed of a determined number of pieces that follow the Fibonacci sequence (1, 1, 2,3,5,8,13), all of them of volume and geometric structure, product of the strategic sectioning of regular polyhedra, of a regular crashed polyhedron and of a sphere, equipped with magnets inside, for the union and assembly between them, with a development of increasing levels of difficulty to stay inside each other and, all, finally, housed in the last of them and that are characterized because each of these systems are composed of six independent sets (C1, C2, C3, C4, C5, C6), and that each independent set is framed with the number of pieces according to the Fibonacci sequence (1, 1, 2,3,5,8,13), and the four independent sets (C1, C3, C4 have regular polyhedra configuration) and C5), of configuration of regular crashed polyhedron, the independent set (C2), and spherical configuration the sixth independent set (C6), emptied internally and with proportional volume to successively accommodate the first in the second, the second in the third, the third in the fourth, the fourth in the fifth, and all in the sixth independent set that has a spherical exterior shape of compact appearance without internal empty spaces.  2. Three-dimensional systems structured by nesting six polyhedra in a sphere respectively, according to claim 1, of said group of independent sets, the first set of regular polyhedral configuration (C1) is characterized in that it consists of several pieces that follow a certain sequence numerical denominated Fibonacci (1, 1, 2,3,5,8,13); tetrahedrally (13) and octahedrally (14). 3. Three-dimensional systems structured by nesting six polyhedra in a sphere respectively, according to claim 2, the pieces (13, and 14) are characterized in that they have magnets (+/-) on their internal faces respectively, strategically oriented each to its opposites (+/-), to ensure a single form of assembly, becoming the smallest independent set of systems mentioned. 2  4. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, according to claim 1, the second independent set with external form of regular crashed polyhedron (C2), is characterized in that it consists of several symmetrical pieces according to the Fibonacci sequence (1 , 1, 2,3,5,8,13), with starry faces formed by tetrahedra (23).  5. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, according to claim 4, the symmetrical pieces (23), are characterized in that when joined they form a pyramidal emptying with square base (24) that allows the millimeter housing of the octahedron (14).  6. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, according to claims 4, and 5, these tetrahedra (23), are characterized in that magnets (+/-) are adhered on their inner faces, one per face respectively, magnetically oriented to their opposites both to the magnets (+/-) of the octahedron (14) and to the magnets (+/-) of the third independent set (C3), which strategically allow a single form of assembly.  7. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, according to claim 1, the third set with polyhedral shape of volume and hexahedral structure (C3), is characterized in that it is made up of several pieces (31, 32 , 33) according to Fibonacci sequence (1, 1, 2,3,5,8,13), which are the product of the strategic sectioning of the hexahedron or cube with an internal emptying in the shape of a tetrahedral star, which allows the exact accommodation of the set (C2).  8. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, according to claim 7, the assembly (C3), is characterized in that magnets (+/-) are strategically oriented, respectively, on the internal faces of their pieces. their opposites, both of the assembly (C2), and the assembly (C4) to achieve a single form of assembly. 9. Three-dimensional systems structured by nesting six polyhedra in a sphere respectively, according to claim 1, the fourth set, with external dodecahedron structure (C4), is characterized in that following the Fibonacci sequence (1, 1, 2, 3.5), consists of several pieces volumetrically reports (41, 42, 43, 44, 45), the same that are the product of a 3 strategic sectioning of the dodecahedron with an internal emptying in the form of an exaggeration, which allows the exact accommodation of the whole (C3).  10. Three-dimensional systems structured by nesting six polyhedra in a sphere respectively, according to claim 9, is characterized in that on their internal faces of said pieces they have attached magnets (+/-) strategically placed and oriented to their opposites in order to form the independent set (C4), as well as adhere to the independent set (C3) as the independent set (C5).  11. Three-dimensional systems structured by nesting six polyhedra in a sphere respectively, according to claim 1, the fifth independent set (C5), is characterized in that it has an external appearance equal to the icosahedron, and following the Fibonacci sequence (1, 1, 2,3,5,8), is made up of several pieces (51, 52,53,54,55,56,57,58), of volume and structure report, product of the strategic sectioning of the icosahedron with an internal emptying in the form of dodecahedron, which allows the millimeter housing of the set (C4).  12. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, according to claim 11, The pieces (51, 52,53,54,55,56,57,58), are characterized in that they are different in the magnetic aspect by the location and polarity of their magnets (+/-), which are attached to their internal faces according to the graph of these pieces, which facilitate the assembly between them as well as the adherence to the independent assemblies (C4) and (C6).  13. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, according to claim 1, the sixth and last independent set (C6), is characterized in that it is the final envelope of the three-dimensional system, which has a general external spherical shape and consists of several pieces following the Fibonacci sequence (1, 1, 2,3,5,8,13). These pieces are divided into two groups; (61) and (62) respectively. 14. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, according to claim 13, the group of pieces (61), are characterized in that they are identical to each other, in volume and structure, but different in the magnetic aspect (+ / -), they are shaped like a spherical cap, and on their internal faces they have attached magnets (+/-) that are magnetically oriented to their opposites, both to those of the same independent set (C6), as to those of the independent set (C5), as detailed in the graphic of the pieces (61).  15. Three-dimensional systems structured by the nesting of six polyhedra in a sphere respectively, according to claim 14, the group of pieces (62), are characterized in that they are identical to each other, in the aspects of volume and structure, but not in the magnetic aspect (+/-), they are shaped like triangular caps with equal edges, and on their internal faces they have attached magnets (+/-) that are magnetically oriented to their opposites, both to the same independent set (C6), as to those of the independent set (C5), as detailed in the graphic of the pieces (62).  16. Three-dimensional systems structured by nesting six polyhedra in a sphere respectively, according to claims 13,14 and 15; the independent set (C6), is characterized in that when solving the independent set (C6), a sphere of compact appearance is formed with an internal emptying in the form of icosahedron that allows the millimeter housing of the independent set (C5), and its solution depends of the correct and unique form of assembly, due to the strategic location of the internal magnets (+/-) of its pieces, since it has thousands of possibilities due to the number of pieces that make up the independent set (C6); and by the number of pieces of the independent set (C5) that is in the position immediately inferior, the possibilities grow to more than a million and a half, thus achieving a high ceiling of difficulty in the assembly of these three-dimensional systems.  17. Three-dimensional systems structured by nesting six polyhedra in a sphere respectively, according to claim 1, the assemblies (C1), (C2), (C3), (C4), (C5), and (C6), They are characterized because, the assembly of these six independent sets in each of the three-dimensional systems, are carried out with coefficients of certain difficulty and comprise up to eleven levels respectively, in which the difficulty varies according to the sequence given in the armed