RU2122080C1 - Polyhedral spheroidal structure - Google Patents

Abstract

FIELD: construction; may be used in erection of spheroidal domes and structures. SUBSTANCE: structure has 50 symmetrical faces of five types. Upper and lower bases are made in the form of regular hexagonal faces. Structure consists of five tiers: equatorial belt having 12 hexagonal faces; two similar belts symmetrical with respect to equator, each belt contains six hexagonal faces is adjacent to base; two similar belts symmetrical to equator, each belt has alternating six pentagonal and six hexagonal faces and is adjacent to equatorial belt. Strength, general stability of shape and space rigidity are ensured due to the fact that structure has four symmetry planes giving by dissection of polyhedron, regular dodecagons in section. In this case, all 96 vertexes of polyhedron are trihedral. Two types of domes may be made on the base of spheroidal structure and its members are presented in state which allows calculation of side lengths and face interior angles with any degree of accuracy. EFFECT: higher strength and stability. 29 dwg

Description

 The invention relates to the construction and is intended for the construction of spheroidal domes and structures. Multifaceted designs are known, approaching in shape to a sphere and an ellipsoid / US patents 4679361, 1987, 4825602, 1989 /, consisting of pentagonal and hexagonal panels.

 The disadvantage of this technical solution is the low structural strength at the vertices of the polyhedra formed by the adjoining of 4 faces. At these peaks, there is a high probability of divergence of the seams of the dome. The most durable assembly of domes is widely known and used, when each vertical seam is overlapped by the face of the next upper belt, for example, the dodecahedron and the truncated icosahedron having trihedral vertices.

 The pentagonal faces located next to the equatorial row are not symmetrical figures, which complicates the assembly of the dome. From an article in Scientific American, 1989, it can be concluded that the dome was calculated sequentially from rings from a polygon, the points of contact of the faces with an imaginary ellipsoid, the lengths of the sides and the internal angles of the faces were randomly selected. This calculation method negatively affects the strength and reliability of the structure as a whole.

 The aim of the invention is to simplify the assembly of the structure, increasing the reliability and strength of the dome.

 The essence of the invention lies in the fact that the multifaceted spheroidal structure contains 50 symmetrical faces of 5 types / Fig. 1, 2, 13 /. The upper and lower bases of the structure are regular hexagonal faces 5 / Fig. 12/.

The design consists of five belts:
- equatorial belt containing twelve hexagonal faces 1 / Fig. eight/,
- two identical belts symmetrically located relative to the equator, each belt contains six hexagonal faces 4 / Fig. 11 / and adjoins the base,
- two identical belts symmetrically located relative to the equator, each belt contains alternating six pentagonal 2 / Fig. 9 / and six hexagonal 3 / Fig. 10 / faces and adjacent to the equatorial belt.

 The polyhedron has 96 trihedral vertices.

 When a polyhedron is mentally dissected by 4 planes of symmetry, 3 planes passing through the midpoints of the sides of the regular hexagonal bases, and 1 plane passing through the equator, in the sections we get the regular dodecagon / Fig. 3-7 /. This design configuration provides strength, overall shape stability and spatial rigidity. The symmetry planes passing through the midpoints of the sides of the regular hexagonal bases give in sections 3 equal to a dodecagon / Fig. 6, section BB. Assuming that the sides of this dodecagon are equal to "a", the elements of the pentagonal and hexagonal faces of the polyhedron are calculated. To calculate the elements of a polyhedron with any degree of accuracy, they are presented in the form of irrational expressions. As a sample, we can give the same representation of convex regular elements / Plato body / and semi-regular / Archimedes body / polyhedra through the length of the side of a regular polygonal face.

и эллипсоид /овалоид/ вращения, близкий к сфере /сфероид/, точки касания поверхности эллипсоида с гранями конструкции находятся на осях симметрии и совпадают, грани 1 и 5 находятся рядом, грани 2, 3, 4 с центрами тяжести граней /фиг. 16 - 18, 20, 21, 22 - 26/. Шестиугольная грань 3 больше пятиугольной грани 2 на величину равнобедренного треугольника с основанием, равным

фиг. 9, 10/. На основе половины конструкции можно получить два типа куполов /фиг. 27, 28/, в основании каждого из которых лежит правильный двенадцатиугольник /фиг. 5, 6, сечения А-А, Б-Б/. Наилучший вариант купола /фиг. 27/, при котором пятиугольники в основании составляют с фундаментом прямой угол, благодаря чему обеспечивается сооружение купола.A sphere with a diameter fits into the design

and an ellipsoid / ovaloid / rotation close to the sphere / spheroid /, the points of contact of the surface of the ellipsoid with the faces of the structure are on the axis of symmetry and coincide, faces 1 and 5 are close, faces 2, 3, 4 with the centers of gravity of the faces / Fig. 16 - 18, 20, 21, 22 - 26 /. The hexagonal face 3 is larger than the pentagonal face 2 by the size of an isosceles triangle with a base equal to

FIG. 9, 10 /. Based on half the construction, two types of domes / FIG. 27, 28 /, at the base of each of which lies a regular dodecagon / Fig. 5, 6, sections A-A, B-B /. The best version of the dome / Fig. 27 /, in which the pentagons at the base make a right angle with the foundation, which ensures the construction of the dome.

Объем конструкции:

Осуществимо изменение высоты и объема конструкции, этого можно добиться, уменьшая или увеличивая длину грани 1 /фиг. 29/.Surface area of the structure:

Scope of construction:

A change in the height and volume of the structure is feasible, this can be achieved by reducing or increasing the length of the face 1 / Fig. 29 /.

 The possibility of carrying out the invention is confirmed by the interest of homebuilding companies in a similar invention and the opening of an advisory firm for its sale in the United States.

 The list of drawings.

 FIG. 1 - front view / main view / multifaceted spheroidal design with the application of the numbers of the faces. Image using the rectangular projection method.

 FIG. 2 is a plan view of FIG. 1 with drawing face numbers.

 FIG. 3 is a sectional view of the structure / image obtained by mentally dissecting the structure by planes of symmetry /, front view.

 FIG. 4 is a plan view of FIG. 3.

 FIG. 5 is a cross section AA passing through the equator of FIG. 3 / regular dodecagon.

 FIG. 6 - section BB passing through the midpoints of the sides of regular hexagonal bases, in FIG. 4 / regular dodecagon.

 FIG. 7 is a cross-section BB passing through the vertices of regular hexagonal bases in FIG. 4 - regular dodecagon.

 FIG. 8 - hexagonal face 1.

 FIG. 9 - hexagonal face 2.

 FIG. 10 - hexagonal face 3.

 FIG. 11 - hexagonal face 4.

 FIG. 12 - hexagonal face 5.

 FIG. 13 - image of the structure in dimetry.

 FIG. 14 - dihedral angles of the structure.

 FIG. 15 - sums of plane angles converging at the vertices.

 FIG. 16 - an ellipsoid to fit into the design. Front view.

 FIG. 17 - points of contact of an ellipsoid with faces. Front view.

 FIG. 18 - an ellipsoid to fit into the design. View from above.

 FIG. 19 - points of contact of an ellipsoid with faces. View from above.

 FIG. 20 - touch points and lines of intersection of a sphere with a diameter equal to the height of the structure with faces. Touch points of an ellipsoid with faces.

 FIG. 21 - touch points from above in FIG. 20.

 FIG. 22 - 26 - centers of gravity of the faces.

 FIG. 27 - dome, image in dimetry. The rational version of the dome.

 FIG. 28 - dome, depicted in dimetry. The second version of the dome.

 FIG. 29 - an increase in the volume of the structure.

Claims (1)

 A multifaceted spheroidal structure containing 50 symmetrical faces of 5 types, characterized in that the structure has upper and lower regular hexagonal bases and consists of 5 belts: an equatorial belt containing 12 hexagonal faces; two identical belts symmetrically located relative to the equator, each belt contains 6 hexagonal faces and is adjacent to the base; two identical belts symmetrically located relative to the equator, each belt contains alternating 6 pentagonal and 6 hexagonal faces and is adjacent to the equatorial belt, while the faces of the polyhedron form 96 trihedral vertices, and when the polyhedron is cut by 4 symmetry planes, 3 planes passing through the midpoints of the sides of regular hexagonal bases and one plane passing through the equator, in the sections you get regular dodecagon.

Images