WO2013048264A1 - Components stamped in low relief with subdivided polygons with flanges on the perimeter thereof - Google Patents

Abstract

The invention relates to a set of stamped components, with subdivided polygons in low relief, with flanges on the perimeter thereof, for manually erecting models of unique geometric convex, concave and solid equilateral polyhedra, specific to special cases, such as special pyramids, modular pyramids and inclined modular pyramids. The components to be connected or assembled are compatible articulated regular polygons and compatible developments thereof. The connection systems are mechanical, magnetic, adhesive and dovetailing systems. The set of components forms a three-dimensional teaching puzzle. The invention requires no prior training, exercises fine motor coordination, teaches geometry through a flexible manual practice, converts abstract concepts into real applications by means of the erection of models, stimulates the creativity, due to its simplicity, rapidity and versatility of handing, promotes self-esteem and develops spatial intelligence in children.

Description

 "PARTS STAMPED IN LOW RELIEF OF SUBDIVIDED POLYGONS WITH

 EYELASHES ON YOUR PERIMETER "

1. SECTOR OF THE TECHNIQUE

The invented device belongs to the Education Sector:

 Teaching and learning of Geometry, by performing exercises aimed at assembling models of geometric solids, assembling pieces embossed in low relief, of sub-divided polygons with tabs on its perimeter.

2. BACKGROUND

ORIGAMI: It is a Japanese ancestral method to structure a sheet of paper in one piece, based on successive and particular folds of a case. With ORIGAMI complicated three-dimensional shapes are constructed. To elaborate these constructions, requires a previous and progressive training, being able to achieve extremely complex harmonic and free forms when practiced and studied as a technique or an art. It is artistic and educational, it is currently used for pedagogical purposes in schools and colleges, because it exercises manual skills and develops spatial intelligence.

PERUVIAN APPLICATION N ° 001074-2005 / OIN: It is a three-dimensional puzzle to assemble models of geometric solids similar to the one we are describing, however, it does not have sub-divided polygons, so its pieces do not transform and their possibilities are relegated. It is educational, it is currently used for experimental pedagogical purposes in schools and colleges. Although it allows to assemble convex and concave equilateral polyhedra, it is not useful for the assembly of unique geometric solids typical of special cases, nor of special pyramids, modular pyramids or inclined pyramids, this lack prevents interesting demonstrations of very easy assembly and understanding, specific for the learning of geometry through the manual assembly of abstract cases, whose understanding is difficult through drawing on the board or in the virtual presentation of a computer. A student who observes a case represented with said request, will then understand the abstractions even if they are presented in virtual form. But you will not be able to access the decomposition of the cube in three tetrahedra equivalent in volume or in twenty four tetrahedra equivalent in volume, to the progression of the cube or tetrahedron, to the modular pyramids, or to the pyramids that make up the five regular polyhedra. The present application exercises manual skills, develops spatial intelligence and facilitates both the teaching and learning of geometry, because the abstract through the assembly of models is made real.

3. BRIEF DESCRIPTION OF THE INVENTION

The invention offers the interested party elaborated parts so that only in the first use, the articulation or transformation folds indicated by the sub-divisions printed in low relief are executed manually. From now on, the number of operations is reduced to joining pieces by their tabs when assembling and disengaging when disassembling the models, in the manner of a three-dimensional puzzle and very quickly. The modular quality of the system facilitates obtaining results quickly. The union of the different pieces by the articulated tabs, is carried out by holding them in pairs by means of their joining systems, these facilitate the manual assembly and disassembly of the models, according to simple instructions.

The set of pieces forms a three-dimensional puzzle, to quickly make models of all known convex equilateral polyhedra, special pyramids, modular pyramids, inclined pyramids, assemble free polyhedral compositions for experimentation, study models or other purposes.

The invention relates to a set of pieces embossed in low relief, of sub-divided polygons with tabs on their perimeter, to be joined in pairs by means of their joining elements. Together the pieces originate a modular three-dimensional puzzle, to manually assemble models of:

 Convex, concave equilateral polyhedra and unique geometric solids specific to special cases, such as:

Special pyramids.- Belonging to a particular case. Example, birect and trirect tetrahedra or the pyramids constituting the five regular polyhedra.

Modular pyramids.- Regular subdivided polygon (except the triangle), with folds embossed in low relief, drawn from the angles to the central point of the polygon (radii). They carry a cut in a radius to overlap one or more central angles. Inclined modular pyramids.- Regular subdivided polygon (except the triangle), with folds stamped in low-relief- drawn from the angles to an eccentric point of the polygon, over the diameter. They carry an overlapping cut.

The patterned sub divisions that delineate polygons also indicate manual bending. The pieces are named after the stamped polygon they exhibit and the location of the subdivisions it presents. Example: Diametral square, radial square, radial pentagon, chordal octagon.

 The sides of the polygons or pieces to be joined have the same measure.

 Each piece has tabs on the perimeter to be articulated by manual folds.

 After the fold, the tabs are articulated and can be held in pairs with their joining systems when assembled or released to disassemble the models.

Sub divisions in the polygons, indicated by folds stamped in low relief, will also be enabled by manual bending.

Depending on the case to be represented of a particular model, it is optional to enable sub division folds. Example:

 With six diametral squares you can assemble a cube, its edges will be the joints of the pieces.

 With twelve diametral squares, after executing the folds in the diametral sub divisions, a larger cube can be assembled, its edges will be the enabled and flexible sub division folds. The unions in this case are located in the diagonals of the faces of the model.

PARTS OF THE PARTS TO OBTAIN

1. PARTS STAMPED IN LOW RELIEF OF SUB-DIVIDED POLYGONS WITH EYELASHES ON THEIR PERIMETER a. COMPATIBLE ARTICULATED REGULAR POLYGON (PRAC) - Laminar piece whose surface has a regular sub-divided polygon with tabs on the perimeter. Example triangular PRAC, square PRAC, pentagonal PRAC, hexagonal PRAC.

Denomination and Definition

1. PRAC tailpiece.- Piece with low relief embossed polygon, whose sub divisions coincide with one or more ropes of the circumscribed circumference. 2. PRAC diametral.- PRAC chordal with a sub division on the diameter of the inscribed polygon, indicates that the polygon can be articulated in two halves. It only applies to polygons with even number of sides. Diametral square example.

 3. PRAC radial.- PRAC chordal with sub divisions on the radii in the inscribed polygon and a cut in a radius.

 With these properly folded pieces, modular pyramid models are obtained by overlapping one or more central angles. Except for the triangle, it applies to every regular polygon.

 4. Decreased PRAC.- Radial PRAC to which one or more central angles have been reduced to become tabs. It allows to represent all the models of modular pyramids of a polygon.

 Except for the triangle, every regular polygon allows to represent as many modular pyramids as the difference between its number of sides minus 3. Example, a heptagonal PRAC originates pyramids with a base of 6, 5, 4, and 3 sides, four pyramids. 7 - 3 = 4.

 5. PRAC perpendicular.- PRAC tailpiece with stamped channel above its height.

 6. Decreased eccentric PRAC.- Cordal PRAC whose sub divisions drawn from each angle converge at a point on its diameter, which is not the center of the inscribed polygon. One or more eccentric angles have been reduced to become tabs.

 Eccentric PRACs are specific pieces to represent models of inclined pyramids, from the pentagon. When the number of sides of the polygon is even, its minimum base will be square, when it is odd the minimum base of the inclined pyramid model will be triangular. b. SPECIAL COMPATIBLE DEVELOPMENT (DEC) .- A laminar piece with eyelashes on the perimeter whose surface is subdivided by a set of articulated polygons specific to a case. They delineate the set embossed folds in low relief that also indicate folds of manual realization.

Denomination and Definition

 1. Regular DEC.- Laminar piece that has two or more PRAC articulated with different denomination.

They may be: to. Regular monkey Polygons of a single type united. Example, chordal square, joined with one or more radial squares.

b. Regular bi. Polygons of two united types. Example, regular triangle joined with radial regular hexagon.

C. Tri regular. Polygons of three united types. Example, radial regular pentagon joined with radial square joined with regular triangle.

 2. Irregular DEC.- Sheet stamped in one piece, presenting several irregular polygons of a type (triangles, quadrilaterals or others) articulated and specific to a case. Example: An irregular tetrahedron model belonging to a special case requires an irregular DEC sheet with two equal right triangles and two equal isosceles articulated to the previous ones, so that the eyelashes with the same dimension coincide after folding, this rare model of Irregular tetrahedron forms in conjunction with the example of the mixed DEC.

 3. Mixed DEC.- Laminar piece whose surface has in one piece, one or more regular and irregular articulated polygons. Example: Sheet with two isosceles right triangles, a regular triangle and a united isosceles triangle, necessary to assemble an irregular tetrahedron model, which belongs to the division of a triangular-based prism, into models of three irregular tetrahedra with equivalent volume.

Parts of a PRAC or a DEC:

Faces.- Obverse and reverse of a piece.

 Sub stamped divisions, articulations or folds of transformation.- Semi-straight mocked or minted by percussion, by a die of marking on the material, to delineate forms of polygons in low relief on the surface of the pieces, which indicate folds of manual realization and Increase versatility in construction possibilities. The execution of the indicated folds, provides flexible rectilinear areas to the material, as well as, allows the assembly of larger models with good structure and particular cases. The folds indicated in low relief are:

1.- Perimetric strings.- Located on the strings, coinciding with the sides of the inscribed polygon, they are modular for all polygons (equal measure on sides to join). 2.- Folds of transformation.- Denominated according to their location:

 to. Ropes, on the ropes.

 b. Diametral, about the diameter.

 C. Radials, on radios.

d. Perpendicular, above the height. and. Eccentric, from the angles to a point of diameter that is not the center of the polygon. ^■

 F. Irregular, delineate irregular polygons.

 Joining tabs.- Appendices or tabs of the polygon located in the perimeter, constitute with this a single piece with perimeter tailpiece articulation, achieved by executing the fold indicated by the stamped cordales folds: Generally with trapezoidal shape, they are used to be held by the elements of the joining systems, when assembling the models. Its external part (obverse) is the contact area between two polygon tabs to be joined, where the adhesive system is placed, its internal part (reverse) serves as a support point for the mechanical joining system and as a location for the system of magnetic union

 Male tab.- Part of the flange enabled as a male, by means of appropriate cuts in a blunt or trapezoid shape, so that a fraction of the flange serves as a connecting element, when penetrating into a complementary groove made on the joint of the flange to be joined.

 Female groove of union.- They are partial cuts made on the articulation of the flange, to house the fraction of the male flange and hold the parts of the model.

2. UNION SYSTEMS: They are the different ways of joining the tabs of the polygons, to form dihedral and assemble the models. They are combined according to the needs of each case. a.- MECHANICAL UNION SYSTEM:

 Pressed Union.-Get the union of polygons by mechanical means type clamp, by holding the tabs by pressing them in pairs. .

 Profile clamp. Elongated element, with a U-shaped section converging at its ends, which structures and secures the tabs of two adjacent polygons by pressure. They are longitudinally rigid and flexible in their section.

 Simple clamp Join with one piece, two tabs of adjacent polygons, in a polyhedron. Side view looks like a rectangle with two of its blunt or rounded corners for easy placement.

Clips.- A pair of conventional clips can replace a clamp. b.- MAGNETIC UNION SYSTEM: Use the magnetic force to hold the parts in the assembly and closing, they are installed on the internal face of the articulated flange of each side of the polygon, elements with magnetic property (active) and sensitive to it (passive) or only active (properly oriented) ).

Universal Magnetic Union (UMU), an adhesive sheet that has a second adhesive sheet attached to it with the exposed adhesive, which has a circular perforation in the center, to accommodate and hold in the perforation, a flattened magnet with the same diameter. A third waxed or silicon removable sheet with the shape of the above, protects the exposed adhesive, it has a pull tab to be removed before use. The dimension and shape of the UMU must be equal to that of the tabs of the stamped polygons because their position is unique. The fixing of the UMU on the back of the tabs of the stamped parts is achieved by means of the adhesive.

 Universal Magnetic Reinforced Union, (UMUR) when the second sheet has two perforations at its ends and has two properly oriented circular magnets attached. It is optional to present a magnet and a magnetism sensitive material

 The UMU or UMUR in the solids models, are placed adhered on the back of the tabs always in the same position, so that when approaching two tabs with UMU or UMUR adhered on the reverse, the position of the oriented magnets or the of the magnets with that of the sensitive material and the magnetic attraction, close the tabs of the stamped pieces.

 The universal magnetic joint system will be located:

 1. In the polygon called the closing polygon, which is the last to be placed in its position in the polyhedron.

 2. In each of the tabs of the polygons adjacent to the closing polygon.

 3. On all tabs at the will of the user or the manufacturer.

 4. On the faces when the project requires it, for example to demonstrate the truncating of polyhedra, (Cube - Cuboctahedron, Icosahedron - Icosidodecahedron).

Gummed magnet, is a magnet with adhesive protected by a removable film, special to be removed before placing it attached on the back of a tab or a face. c- ADHESIVE UNION SYSTEM:

Use adhesive means to secure the parts in the assembly, incorporating to the external face of the articulated flange of each side of the polygon, adhesive material or glue. The adhesive bonding system is combined with the mechanical bonding system to hold the joints until dry or as reinforcement as appropriate. Permanent adhesive system It is achieved by applying permanent adhesive to join two tabs.

 Removable adhesive system.- It is achieved using removable adhesive (reusable) to join two tabs.

Protected adhesive system.- It employs a silicone or waxed sheet-shaped material protector with a shot appendage, located on the adhesive to keep it or between two adhesive tabs to temporarily join pieces and be able to detach the joints when disassembling the representation. It is also applied in the magnetic bonding system. d.- MACHIHEMBRATED UNION SYSTEM

 Tongue-and-groove Union.- Use the tabs enabled as male and female grooves in the joints to join the pieces.

 Male tab.- Part of the flange can be enabled as a male by means of appropriate cuts so that a fraction of the flange serves as a joint element when penetrating a complementary groove made on the articulation of the neighboring face.

 Female groove of union. - They are partial cuts made on the articulation of the flange, to house the fraction of complementary male flange and hold the parts of the model.

Advantages of the invention, compared to other known ones:

 to. It does not require prior training.

 b. Exercise fine motor coordination.

 C. The learning of geometry is achieved through an agile manual practice

 d. The abstract by arming models is made real.

 and. Stimulates creativity by its simple, fast and versatile operation.

 F. Raise self-esteem

 g. Develop the child's spatial intelligence.

4. RELATIONSHIP AND DESCRIPTION OF THE FIGURES:

Figure 1: Regular articulated compatible polygons, or PRAC, triangle, square, pentagon and hexagon.

Figure 2: PRAC, with stamped folds; diametral in the square and the hexagon, strings in the pentagon. Figure 3: PRAC, square, pentagon, hexagon with radial bends and a radial cut.

Figure 4: PRAC, regular triangle with perpendicular fold. Figure 5: PRAC, square, pentagon and hexagon without a central angle (reduced to tabs) to achieve modular pyramids.

Figure 6: Modular pyramid of the pentagon with square base. Figure 7: Mechanical joining system, two clamps or joining profiles, join three polygons.

Figure 8: Modular pyramid of the octagon with hexagonal base.

Figure 9: Tetrahedron with diametral hexagons in its dihedral.

Figure 10: Three cubes, the upper one and the lower one with trirect pyramids in their corners or vertices, (modular square pyramid).

Figure 1 1: Progression of the cube. Diagonal of the upper cube equal to the side of the lower cube.

Figure 12: Truncated octahedron with hexagons folded in half, located in its dihedral, the PRAC is a hexagon with diametral fold used to achieve an obtuse dihedral.

Figure 13: Truncated octahedron, the PRAC is a hexagon with diametral fold used to achieve an obtuse dihedral

Figure 14: Armored cube with fourteen stamped squares, eight radial PRACs (converted into trirect, modular square pyramids) located in the corners and six diametral squares located in the shape of a rhombus.

Figure 15: Cube and cuboctahedron, derived by truncating or cutting its corners.

Figure 16: Cube armed with twelve square diametral pieces, the diametral folds are their edges, the joints of pieces are located in the diagonals of their faces. Figure 17: Cube built with six diametral squares. Figure 18: Octahedron. Figure 19: Icosahedron. Figure 20: Dodecahedron. Figure 21: Tetrahedron with fractional faces.

Figure 22: Helicohedron, polyhedral composition that represents a wave with a horizontal axis rotation effect. Result of the experiment with polyhedra.

Figure 23: Eccentric decagon with overlapping cut.

Figure 24: Decreased eccentric decagon.

Figure 25: Octagon with radial folds and a cut for overlap. Figure 26: Octagon with additional perpendicular parallel chordales folds.

Figure 27: Special compatible mixed development or mixed DEC, three irregular polygons linked with a regular one. Figure 28: Irregular DEC, four irregular polygons, joined.

Figure 29: Polygons with tongue and groove tabs.

Figure 30: UMU universal magnetic union and UMUR reinforced.

Figure 31: Gummed magnet.

Figure 32: Birerect tetrahedron or single inclined pyramid, obtained with diametral square PRAC, its volume is equivalent to that of the regular tetrahedron, when both have the same base and equal height.

Claims

1. Pieces stamped in low relief, of subdivided polygons that have trapezoidal folds and tabs on their perimeter, which originate compatible articulated regular polygons (PRAC), to be joined or assembled with their joining systems, characterized in that the subdivisions or folds stamped in low relief, they transform the piece when executed manually and they are, PRAC chordal, PRAC diametral, PRAC radial, PRAC diminished, PRAC perpendicular, PRAC eccentric and PRAC eccentric diminished. 2. Pieces stamped in low relief, of subdivided polygons according to claim 1, characterized in that a radial fold is cut. 3. Pieces stamped in low relief, of subdivided polygons, according to the preceding claims, characterized in that a laminar piece with flanges on the perimeter whose surface is subdivided by a set of regular, articulated compatible polygons, is a compatible special development (DEC ) regular. 4. Pieces stamped in low relief, of subdivided polygons according to claims 1, 2 and 3, characterized in that a laminar piece with flanges on the perimeter whose surface is subdivided by a set of irregular, articulated compatible polygons, is a special development compatible (DEC) irregular. 5. Pieces stamped in low relief, of subdivided polygons according to claims 1, 2, 3 and 4, characterized in that a laminar piece with flanges on the perimeter whose surface is subdivided by a set of regular and irregular, articulated compatible polygons, It is a special compatible development (DEC) mixed. 6. Parts embossed in low relief of subdivided polygons according to claim 1, characterized in that the joining elements are selected from the systems: mechanical, magnetic, adhesive and tongue and groove. 7. Parts embossed in low relief of subdivided polygons according to claim 6, characterized in that the mechanical joining system is clamp type. 8. Parts embossed in low relief of subdivided polygons according to claim 6, characterized in that the tongue and groove joint system employs tabs enabled as males and partial cuts enabled as females in the joints to join the stamped pieces. 9. Parts embossed in low relief of subdivided polygons according to claim 6, characterized in that the magnetic joint system employs the Universal Magnetic Union (UMU), an adhesive sheet that has a second adhesive sheet attached with the exposed adhesive, which has in the center a circular perforation, to accommodate and hold in the perforation, an oriented magnet, flattened with the same diameter, a removable sheet with appendage, protects the exposed adhesive. 10. Parts embossed in low relief of subdivided polygons according to claim 9, characterized in that the magnetic bonding system employs the Universal Reinforced Magnetic Union, (UMUR), adhesive sheet that has a second adhesive sheet adhered to the exposed adhesive, the which has at the ends two circular perforations, to accommodate and hold in the perforations, two magnets oriented and flattened with the same diameter, a removable sheet with appendage, protects the exposed adhesive. It is optional to present a magnet and a material sensitive to magnetism in the perforations, which avoids orienting the magnets. 11. Parts embossed in low relief of subdivided polygons according to claim 9, characterized in that the magnetic bonding system employs Gummed Magnet, a circular magnet oriented and flattened with exposed adhesive, a removable film with an appendage, protects the adhesive.