DE19535636A1 - Sports ball with casing formed from basic shapes - Google Patents

Abstract

Football or other sports ball in which the casing surface (0) is built up from circular to elliptical basic shapes (1) using regular polygons. At least six or a whole number multiple of six basic shapes are drawn together such that their contours can be sewn or joined in the form of closed polygons (P) with at least ten sides/corners. The basic shapes can be composed of facets/facet patterns (2).

Description

The invention relates to a hollow body, ball, game / sports ball, in particular Football, with a convex, preferably spherical to ellipsoidal envelope surface / Shell, which according to the specification circular to elliptical basic pattern shapes in (regular) polygons structured, patterned, covered, covered, coated, glued and from it is made.

The hollow body, in particular the ball, is characterized in that at least twelve, or a multiple of six such basic pattern shapes used, used or are available, their contours not necessary but preferably in the form of closed polygons at least ten sides / corners are approximated or screened. Without prejudice to this, it can also be used for certain applications (e.g. radomes) only part of the sphere or ellipsoid is used, and then Such a closed polygon can also be open (e.g. by separating).

An important - if not exclusive - area of application are balls of all kinds. Also tanks isolated from coverings or from Shell composite fabricated shell constructions, as well as dome roofs or patterns on tableware service such as bells, terrines, can do so for example, can be found and varied.

According to the state of the art for game and sports balls such as Tennis, football judged, the following product designs mainly enforced:

• - Two-part tennis ball with identical facets:
  with a small diameter of approx. 6.5 cm, parts still have to be manageable, therefore only two relatively small parts that can also be easily shaped without the ball becoming out of round.
• - Football, developed from a dodecahedron, by 12 pentagons the pentagon is suitably divided to z. B. 12 smaller pentagons included, each surrounded by five "3-stars", a total of 20 pieces, so that a 32-part ball is formed, according to DE 37 26 830.9-15

Another, most common soccer variant is the one from 12 Pentagons and 20 hexagons existing "standard" ball. Again, the ball has a total of 32 facets in two basic patterns.

In general, there are only one of the regular polyhedra Facet shape only dodocahedron (12 pentagons) and icosahedron (20th Triangles) are available, with the only 12- or 20-part football  Diameters of about 21 cm is still too roughly structured to be high To be able to meet roundness requirements because of the dissolution of the surface is only slight, so the individual facet is not particularly handy / flexible is, therefore, is usually too strongly deformed / stretched at the corners, to take a reasonably round shape.

The above two ball variants were previously available for soccer balls, so we were able to - albeit a few - faceted variants can be found from it. The game ball (dto. Balloons) on the meridional triangle segments is also after still popular, since simple solutions for the flat facet shape have been here are known for a long time (great circles, globe model / cartography).

The hollow body, ball, sports ball, in particular football, according to the invention, offers u. a. in the metal sector, such as boiler construction (insulation), in particular good, tailor-made variations in air sports and ball sports and possible uses, with hollow body dimensions, maximum permissible Cutting dimensions of the machines and webs used are. As well as usage and economic aspects, degree of roundness achievable in this way, high symmetry, number of (different) Parts, entire seam length to give examples of such criteria.

Circular, elliptical patterns and / or facets - also or in particular when resolved into regular polygons - are balanced in dimensions, easy to calculate mathematically and geometrically, but only few parameters such as B. Radius (semi-axes) are to be varied, in addition Angular and circumferential division. Even when mapping circular to elliptical formation of hollow body surfaces on the material level and conversely, there are advantages. Circles and ellipses, even if offer polygonized with tight packing of the flat cutting material a high degree of material utilization are resources and costs saving. When buying products in capital goods as well as in the consumer goods sector the eye also reacts to high symmetries, as experience has shown that these are be perceived as particularly pleasing, nature seems to be a role model. This will result in faster refinancing of development investments more likely through stronger demand.

Above all, however, high symmetry means advantages for manufacturing such as Quality assurance: the flat and spherical decagon is very regular and therefore particularly low warpage with the same center angle of 36 degrees.

On the spherical ball from 30 identical rhombus facets found is the such a high symmetry is clearly recognizable (shapes, arrangements).  

According to the invention, regular hollow bodies such as Spheres and ellipsoids, also barrel bodies, are typical rotations Dissolve, divide, pattern or dissolve the surface of the body as follows assemble, described using the example of the ball.

In accordance with the invention, closed hollow bodies or their open parts / Shells / covers - such as containers, balloons, umbrellas, parachutes, Brake umbrellas, balls (tennis ball, soccer, rugby ball, for example) or tent and roof-like structures - from limp or rigid materials of all The way of manufacturing is an essential design step or manufacturing step required:

• 1. formation of a spherical cap / a spherical segment, e.g. B. with opening angle 2 × 30 ° (12 × 30 ° = 360 °)
• 2. Determination of central angle and outer angle for formation regular polygons when polygonizing the spherical cap (a circular basic pattern shape in plan view). Example decagon: central angle / external angle = 36 °
• 3. Arrangement of 12 such circular basic patterns the surface z. B. side parallel side on gap or touching, where touching a side center of the one basic pattern shape meets a corner of the adjacent basic pattern shape. When touching in sections, polygon sides meet the circular ones Basic pattern shapes in pairs.
• 4. The rest between the basic pattern forms Surface pieces complement the spherical surface and can be like that Basic pattern shapes or their polygons are facets / facet patterns.
• 5. By - also gradually - any subdivision of the basic pattern forms, the polygons or their suitable combination can contain facets / Facet patterns can be found according to specific requirements. For example, a ball can consist of 30 identical diamonds be composed. These can be in their dimensions can be found in particular in that two, with common polygon touching decagon in five equal parts (Central angle in the projection 72 degrees) divided and summarized so that a rhombus is obtained by the resulting two spherical triangles are combined, the common sphere triangle side is diagonal of the (spherical) rhombus.  
• 6. By suitable mathematical (piecewise) mapping of the polygons or facets / facet patterns - such as the rhombuses - into the Material level, for example, flat stampings for the ball win manufacturing. The polygons can also be advantageous in Sphere triangles (sum of angles greater than 180 °) divided, disassembled and are depicted as such.

In this way, spherical or ellipsoid can be particularly easily Add hollow bodies made of facets or sample facet-like or colorize. However, any other surfaces, too not included in the basic description here.

The illustrations below show an example of an illustrated one Selection of typical options for obtaining the invention Hollow bodies, balls, sports balls, in particular soccer balls and game balls.

Modifications not shown are according to the invention with the above Steps listed, as well as shown, are:

Fig. 1a spherical hollow body, ball, divided according to circular basic pattern in, for example, here 12 regular decagonals, simplified 3-D view (without enveloping outer contours due to hidden basic pattern on the back).

Fig. 1b Elliptical / lenticular hollow body, ball, divided according to the circular basic pattern into, for example, 12 decagon here, simplified 2-D view (without enveloping outer contours due to hidden basic pattern on the back).

Figure 2a x. A 2-D view, y of a spherical hollow body, with the ball portion wise contact of the pattern shapes, here in pairs with a common edge decagon.

Figure 2b is another 2-D x. View, y of a spherical hollow body, ball with separate pattern shapes, such as emerged as by the contraction of Fig. 2a.

Fig. 3a 2-D view of a spherical hollow body, ball with further subdivided basic pattern shapes, here decagon with five identical sections within individual basic patterns.

Fig. 3b 2-D view of another spherical hollow body, ball with a subdivision of the basic pattern shapes over several basic pattern shapes, here two decimal corners form a rhombus, 5 rhombuses a pentagon-like structure.

Fig. 4 Another comprehensive summary as before, now two decagon pages included in the facet pattern formation.

FIG. 5a is a 2-D view with example 20 not further divided segments between here contacting pattern shapes.

Fig. 5b is a 3-D view of a hollow body, with the ball 12 and 20 Zehneck- segment facets according to the basic pattern shapes.

Fig. 5c is a 2-D view of a hollow body, the ball in a modified embodiment with 12 other Zehneck- and 20 segment facet / facet patterns in accordance with the pattern shapes, another derived therefrom alternative with 12 pentagons and 20 scalene Secksecken is partially indicated by broken lines ( Repetitions).

FIG. 5d shows a 2-D view of a hollow body, ball, with this separate base pattern shapes, and a three star-like patterning disposed around the substantially triangular appearing segment core.

FIG. 5e, a 2-D view of a hollow body, ball, with here also separated from each other pattern shapes and a decagon oriented patterning, here along each second edge, and here within each polygon decagon (can also be considered a modification of the variant of FIG. 5d be construed) .

FIG. 6a, b a grouping 5 same diamonds in Pentagon formation; if facets, z. B. a 30-part ball can be produced with a single type of facet, Fig. 6a.

Fig. 6b is a modification of the facet shape.

Fig recovered. 7a-e other types spherical hollow body, ball, in particular soccer ball, from in Fig. 6a, b regular rhombs shown, also derived from the same basic pattern Zehneck- forms.

Fig. 8 shows another possible variant of a circular basic pattern, resolved into a decagon polygon, and further regularly divided into the same parts, here enclosing a pentagon.

The exemplary hollow bodies of all kinds, in particular Ball, game ball, sports ball, show the principle to be followed Providing circular or elliptical basic shapes applied to spherical and / or ellipsoid and ellipsoid-like as well as barrel-shaped Hollow bodies, various patterns, facets, assignments structure and manufacture. Since the ball is just a special case of Ellipsoids are, the aforementioned and following explanations apply analogously for the ellipsoid or similar body as well as their Parts. In practice, the sphere is the most important Use case, is therefore preferred and for reasons of simplification shown, the range of variation is thus set out.

Fig. 1a is a spherical hollow body, ball, the envelope surface 0 according to circular basic pattern shapes 1 in here, for example, twelve regular polygons 1 'is gridded as a decagon. The simplified 3-D view is shown without the spherical contours, whereby the front six hexagons (including diagonals) do not touch and therefore the hidden six hexagons are partially visible in the gaps.

Fig. 1b shows an ellipsoidal hollow body, ball, the envelope surface 0 according to circular basic pattern shapes 1 , with reference to the ball of Fig. 1a also, for example, twelve regular polygons 1 'in the form of decagons (closed polygons P) is rastered.

Fig. 2a shows a 2-D view x, y of a spherical hollow body, ball with partial contact of the basic pattern shapes 1 / polygons 1 'of the envelope surface 0 , with paired common decagon edge K.

Fig. 2b shows another 2-D view x, y of a spherical hollow body, ball with edges K of the basic pattern shapes 1 / polygons 1 'now separated from one another, as emerged, for example, by their contraction from a hollow body of Fig. 2a (upper half shown) .

Fig. 3a shows another 2-D view of a spherical hollow body, ball, now with further subdivided basic pattern shapes 1 , here as a decagon - polygon 1 'with five identical sections A within individual basic pattern shapes 1 , indicated as an example for a selection of the same.

Fig. 3b shows in a 2-D view of another spherical hollow body, ball, now a subdivision of the basic pattern shapes 1 over several basic pattern shapes 1 or polygons 1 '. Here, two adjacent decagon polygons 1 'form a rhombus R. 5 such rhombuses R thus, as highlighted, form a pentagon-like arrangement and envelope surfaces 0 structure.

Fig. 4 shows another cross-shape pattern shows a further modification 1 Summary, similarly as above, now across two opposing edges Zehneck polygon 1 K.

FIG. 5a is a 2-D view of decagon shows polygons 1 'now, for example 20 not further divided segments 4 between here contacting pattern shapes 1. The segments 4 can be spherical triangles D as highlighted by blackening. In a modification of the decagon polygons 1 '- for example over the side centers of the inner pentagon auxiliary lines indicated by dash-dotted lines - such a segment 4 can be modified into a hexagon as indicated by broken lines, polygons 1 ' having a more "snowflake-like" structure being formed here with 15 corners and edges, as shown on the central polygon 1 '. Unless all polygons 1 'are identical, a rhombic segment 4 is "conceivable".

Fig. 5b is a 2-D view of a hollow body, ball with 12 decagon basic pattern shapes 1 and 20 segment 4 facets, which arise in accordance with the basic pattern shapes 1 when they are shrunk towards their center on the envelope surface 0 .

This makes it possible to gain more T- to X-shaped segment 4 facets, the contours of which are given by the three to four adjacent decimal polygons 1 '.

Fig. 5c is a 2-D view of a hollow body, in a modified embodiment with ball 12 and 20 other Zehneck- segment facet / facet patterns 4 in accordance with the pattern molds 1.

Another alternative derived therefrom with 12 pentagons and 20 here unequal segments 4 is partially indicated with broken lines (repetitions), but then the polygon 1 'is again a decagon, which is rotated against the basic pattern 1 decagon polygon 1 '.

Fig. 5d a further 2-D view of a hollow body, ball, with this separate base pattern molds 1, and a three-star-like patterning to the substantially triangular appearing segment 4 core.

Fig. 5e is a 2-D view of a hollow body, ball, with here also separate basic pattern shapes 1 and a decagon-oriented pattern or structure, here along every second edge K and here within each decagon polygons 1 '(can also be a variant of the variant to Fig. construed 5d).

Fig. 6a represents a grouping of five identical rhombuses R in a pentagon formation, which, as indicated in Fig. 3b, are obtained from the decagon polygons 1 '. If these diamonds are R facets 2 , z. B. a 30-piece ball can be made from a single type of facet. The one central angle of such a spherical rhombus in the grouping is 72 ° (360 ° in total) for the ball. As is known, a rhombus R has louder sides of equal length.

6b by contraction of each of a diagonal blank. In a modification of Fig. 6a form other symmetrical here facet / facet pattern 2.

To illustrate this, a rhombus R is four times wider (in rhombuses) divided.

Fig. 7a-e another type of spherical hollow body, ball, in particular soccer ball, obtained from regular rhombuses R shown in Fig. 6, in particular derived from the same decagon polygons 1 '. For balls these facets / facets pattern 2 are particularly advantageous because of the uniformity of distribution of envelope surface 0 and the balance of diamonds R.

Fig. 7a shows a 30-piece ball same rhombuses R, BR in a 2-D view. In the center, five rhombuses R / base rhombuses BR are combined in a ring to form a pentagon-like "snowflake" structure. Together with another five rhombuses R / base rhombuses BR arranged around it, a superordinate pentagon-like structure is formed from 10 rhombuses R / base rhombuses BR. When the hollow body is rotated, these structures can be recognized again and again, unless they are identified as such by patterning, for example as a five-leaf / maple leaf.

Fig. 7b shows a 12-piece ball same rhombuses R, BR, caused by Summary of 2.5 rhombuses BR in such a way that in each case a rhombus is divided into two (spherical) triangles D.

Fig. 7c shows a 6- (12, 24) the same piece ball diamonds R, BR, caused by Summary of 5 lozenges BR. These facets / facet patterns 2 are doubly symmetrical (12 and 24 parts are also possible) and therefore contain the pairing of the polygons P according to FIG. 7b.

FIG. 7d shows a 3- (6-) part ball of the same rhombus R, BR, which is created by combining 10 (5) rhombuses BR, two identical facets / facet patterns 2 according to FIG. 7c being joined together (rotated arrangement).

FIG. 7e shows a further 3- (6-) part ball of the same rhombus R, BR, which is created by another combination of 10 (5) rhombuses BR into facets / facet patterns 2 .

Fig. 8 is shown another possible variant of a circular basic pattern shape 1 , in a decagon polygon 1 ', and regularly divided into the same, here a pentagon enclosing sub-pattern 6 (4''').

In this way, solutions are tailored according to the invention provided for balls of all kinds and other hollow bodies such as containers, Balloons, umbrellas, etc., which, depending on the application requirements, consist of some few or many facets can be produced flexibly, in particular spherical triangles (as constructive elements of the facets) one Calculation of angles and side lengths are easily accessible.

All in all, it becomes a simple and economical process Design and manufacture of hollow body surfaces from facet shapes which is equally suitable for sampling the same.

Result:
Starting from the ball with 12 identical decagonals, a whole "class" of envelope surfaces or hollow body / ball facets is found by dividing the decagon polygons according to the invention into rhombuses consisting of two combined triangles.

• - First, there are variations of decagon facets Hollow body found, starting from 32 parts.
• - Secondly, by different grouping the unchanged Rhombi, starting from 30 equal parts, especially hollow bodies with 15, 10, 6, 3, 2 parts found.
• - Third, the division of the rhombuses, for example, the 12-part Hollow body found. Finer subdivisions are special possible recursively, again with rhombuses and / or triangles arise.

The most important rhombus application for tennis balls is the 2, 3 and 6- be part hollow body.

In football with few parts, for example, 6, 10, 12, 15 Polygons formed from rhombuses - also with smoothed polygons - Can be used next to the 30-piece ball.

With this by no means complete range of solutions according to the invention for the hollow body, ball are progress in targeted development possible according to specific industry requirements, especially for regular assignments with manageable sizes all the way to the divisions the dimensions of the hollow body (tanks, for example) can be adapted.

Claims (24)

1. Hollow body, ball, game / sports ball, especially football, with a convex, preferably spherical to ellipsoidal envelope surface ( 0 ), characterized in that the envelope surface ( 0 ) in accordance with circular to elliptical basic pattern shapes ( 1 ) in - preferably regular - Polygons ( 1 ′) structured, thus patterned, covered or produced, and characterized in that at least twelve or an integral multiple of six such basic pattern shapes ( 1 ) are used or are present, the contours of which are preferably in the form of closed polygons (P) are approximated or screened with at least ten sides / corners. 2. Hollow body, ball, game / sports ball, in particular football according to claim 1, characterized in that the basic pattern shapes ( 1 ) are used indirectly or directly for the determination, generation, production of facets / facet patterns ( 2 ) and / or other patterns or Find use, the basic pattern shapes ( 1 ) themselves can also be such facets / facet patterns ( 2 ). 3. Hollow body, ball, game / sports ball, in particular football according to claim 1, 2, characterized in that the hollow body has a spherical or rather spherical envelope surface ( 0 ) and the basic pattern shapes ( 1 ) themselves form facets / facet patterns ( 2 ). 4. Hollow body, ball, game / sports ball, in particular football according to claim 1-2, characterized in that the hollow body has an ellipsoidal or rather ellipsoid-like envelope surface ( 0 ) and the basic pattern shapes ( 1 ) themselves form facets / facet patterns ( 2 ). 5. hollow body, ball, game / sports ball, in particular football according to claims 1-4, characterized in that the basic pattern shapes ( 1 ) touch point by point or in sections. 6. hollow body, ball, game / sports ball, especially football according to claims 1-4, characterized in that the basic pattern shapes ( 1 ) are separated from each other. 7. hollow body, ball, game / sports ball, in particular football according to claims 1-6, characterized in that the individual basic pattern shapes ( 1 ) are further structured into parts ( 3 ) or dissolved. 8. Hollow body, ball, game / sports ball, in particular soccer ball according to claim 7, characterized in that the parts ( 3 ) from only one or more basic pattern shapes ( 1 ) are obtained, combined to form facets / facet patterns ( 2 ) or added. 9. hollow body, ball, game / sports ball, especially football according to claims 1-8, characterized in that the basic pattern shapes ( 1 ) are the same or identical. 10. Hollow body, ball, game / sports ball, in particular football according to claims 1-9, characterized in that the basic pattern shapes ( 1 ) are structured, dissolved, summarized or added in the same way according to claim 7, 8. 11. Hollow body, ball, game / sports ball, especially football according to claims 1-10, characterized in that there are at least 20 segments ( 4 ) between touching / non-touching basic pattern shapes ( 1 ) or facets / facet patterns ( 2 ), wherein these themselves can also be divided, in particular in the case of claim 5, can also be summarized. 12. Hollow body, ball, game / sports ball, in particular football according to claims 1-11, characterized in that the segments ( 4 ) are single or multiple symmetrical. 13. Hollow body, ball, game / sports ball, in particular soccer ball according to claim 11, characterized in that the segments ( 4 ) or segment pieces ( 4 ) have triangular, rather circular or rather elliptical contours - elliptical contours particularly arise when from circular contours obtained by transferring an already patterned spherical surface by scaling one or two main axes into a "terrine to plate-shaped" hollow body with such a partly round, partly elliptical main view or an ellipsoid. 14. Hollow body, ball, game / sports ball, in particular football according to claims 1-13, characterized in that the envelope surface ( 0 ) each has a single facet pattern ( 2 ), which is not necessarily but preferably congruent / identical in shape, especially in the case of spherical closed or open hollow bodies (parts). 15. Hollow body, ball, game / sports ball, in particular soccer ball according to claim 14, characterized in that the facet / the facet pattern ( 2 ) is a rhombus (R), at least thirty such rhombuses (R) covering the entire envelope surface ( 0 ) form, the rhombus (R) can be further subdivided, for example into rhombuses (R) or into triangles (D), for example. 16. Hollow body, ball, game / sports ball, especially football according to claims 1-15, in particular according to claims 14, 15, characterized in that - starting from 30 identical rhombuses (R) - closed polygons (P) of the same type can be found in that this polygon (P), which is therefore called the base rhombus (BR) either summarized further, or preferably only once, is divided in particular into two triangles (D) or successively, preferably also recursively in rhombuses (R). 17. Hollow body, ball, game / sports ball, in particular football according to claim 16, characterized in that the rhombuses (R) can be distorted, while maintaining the structures without distortion, in particular while maintaining / invariance of the area dimension of the envelope surface ( 0 ). 18. Hollow body, ball, game / sports ball, in particular football according to claim 16, characterized in that the summary of the rhombuses (R) is based on the (prime number) decomposition (Z) = 30 = 1 × 2 × 3 × 5, wherein in particular spherical envelope surfaces ( 0 ) according to an education law from a collection of in particular 30 × 1, 15 × 2, 10 × 3, 6 × 5, 3 × 10 or 2 × 15 identical polygons (P), or facets / facet patterns ( 2 ) , exist, are formed or patterned, obtained as a summary of the basic rhombuses (BR) according to the application of the formula according to the invention:
Polygon number N divided by divisor,
wherein the polygon number N is preferably 30 or, if the base rhombus (BR) is divided, a multiple thereof and the divisor consists of individual factors or products of parts of the (prime number) decomposition (Z) or of this itself. 19. Hollow body, ball, game / sports ball, in particular football according to claim 16, characterized in that when combining 2.5 base rhombuses (BR) - half the base rhombus (BR) is broken down into two triangles (D) - 12 identical polygons (P) and / or facets / facet patterns ( 2 ) are created, in particular a 12-part envelope surface ( 0 ). 20. Hollow body, ball, game / sports ball, in particular football according to claims 1-19, in particular 1-15, characterized in that several, in particular five adjacent basic pattern shapes ( 1 ) form superordinate such polygon structures ( 5 ) which are formed by regular polygon patterns, are encased in particular by pentagons, such groups of polygon structures ( 5 ) being successively outwardly enveloped again by in particular other polygon structures ( 5 ) of the same type or could be enclosed (recursively) with them. 21, hollow body, Ball, play / Sport Ball, in particular Rißball according to claims 1-20, in particular 1-16, characterized in that the individual pattern shapes is dissolved (1) congruent in a number of equal / sub-pattern (6). 22. Hollow body, ball, game / sports ball, in particular soccer ball according to claim 21, characterized in that the same / congruent partial patterns ( 6 ), joined together along the basic pattern shape ( 1 ), have closed edge curves, the inner edge curve not being necessary to the point degenerate, so that even the edges of other enclosed, not identical, sections can be. 23. Hollow body, ball, game / sports ball, especially football according to claims 20, 21, 22, characterized in that pentagons (pentagons) are repeated / successively form enveloping or superordinate enclosures. 24. Hollow body, ball, game / sports ball, in particular soccer ball according to claims 1-23, characterized in that the envelope surface ( 0 ) any, in particular metallic or non-metallic material, are prefabricated and arched and by known joining and connecting techniques, so for example vulcanizing, sewing, gluing, welding, soldering, riveting, laying, laminating and the like, with or without a fold to be connected to the complete or partial convex, spherical or ellipsoside-bearing, shaping or covering surface, single-layer or multi-layer, the layers not necessarily must be identical in the facets / facet patterns ( 2 ), and the interior of the hollow body can also be completely or partially filled in solid, liquid or gaseous.