the spherical building block of the present invention is derived from a cube and is , itself , the product of a plurality of squares folded and assembled to form the individual subunits that are joined together to form the intersecting rings . to form a spherical building block 1 having a circumference c according to the present invention , cut 36 squares measuring along side a = ⅛ of the circumference c ( fig2 ). group the squares in 18 pairs in the following way : rotate each square in a pair to be 45 ° relative to each other to form an eight point star , bend the corners of the upper square 2 downward and the corner of the lower square 3 upward as shown in fig3 a and join each pair only by their adjacent borders . after the union you have a subunit 4 , as shown in fig3 b , with two flat lids ( each one measuring a /√ 2 ) and four fitting angles on the sides forming a periphery of eight interdigitated triangles 5 or angular faces , whereby the opposing triangles 5 of the lower square 3 form each of the fitting angles 6 ( fig3 b ). to permit eight of the subunits 4 to combine to form a ring 9 , the fitting angles 6 have to be adjusted to an external angle of 45 degrees , which obliges the exterior lid or upper surface 7 to adopt a semispherical curvature while the interior lid or lower surface 8 remains flat . eight of the subunits 4 are then joined at adjacent angular faces or fitting angles δ to form a complete ring 9 with eight subunits 4 ( 45 °× 8 = 360 °). the ring 9 is repeated around each axis of the sphere 1 ( xyz ) to form three intersecting rings 9 with eighteen pieces or subunits 4 ( fig1 a , b and c ) thereby producing one complete spherical building block with each ring being orthogonal to the other two and having its geometrical center at the center of the resulting spherical building block and corresponding to the center of the xyz coordinate system . this procedure is so simple since the nature of the square contains in its proportion the capacity to form spheres , or substantially spherical bodies 1 . it is the exact relation between the side and the diagonal , what allows the thirtysix squares to form a union system that is perfectly symmetrical and exact . fig1 a , b and c , show three points of view for the building block , x , y and z , and the corresponding rings x , y and z made up of the subunits 4 . this patent application is related to applicant &# 39 ; s copending application ser . no . 10 / 398 , 405 titled cover for ball or sphere , originally filed as pct / cr00 / 00003 , filing date oct . 10 , 2000 . which describes a surface scheme based on the similar principal of eighteen squares to form a sphere . this surface scheme states the symmetrical accommodation of eighteen square pieces with diagonals measuring d = ⅛c ( note that ⅛c = a , but we will later see how d = a ). the squares 2 that correspond to the described semispherical upper surfaces 7 of the subunits 4 are joined along their diagonals forming a circle or ring 9 of eight subunits 4 around the axes ( x , y , z ) as shown in fig1 . even though three circles or rings 9 of eight subunits 4 add up to twenty four pieces or subunits 4 , the sphere 1 can be built with eighteen subunits , since the rings 9 share subunits 4 in six intersections . these six intersection subunits are called x ( fig1 a ) because the letter represents the crossing of the two directions . the other twelve subunits are called z ( fig1 c ) because this letter represents the ecliptic . when accommodating the subunits in three circles you are assuring that each ring 9 will have an identical circumference c1 and you can perfectly define the eight octants . the calculation difficulties present themselves in the determination of the central point y of the octant . if the six centers x or intersection subunits represent a cube &# 39 ; s faces , the eight centers y corresponding to cavities 12 are equivalent to the corners of the cube . furthermore , the “ not ” intersected subunits z are located in the borders of the cube in an intermediate zone between x and y . the following summarizes the terms and formulas used in calculating the squares used to make up the subunits for rings and a sphere of a particular circumference c : ½c × { square root over ( 3 )} = 3 / 2 ( d − a ) and if the ecliptic is fixed altering only c2 = 5 . 5213 . . . %, then c1 = c2 = c3 . it is important to clarify some concepts and ideas of applicant &# 39 ; s copending application to help determine the characteristics of the inward extending cavities of the spherical building block of the present invention . in that document we mention that 18 black squares represent the true surface of the cube and the rest of the white pieces constitute empty space . a more certain explanation in the case of the building block of the present invention is that the white pieces are folded towards the interior of the sphere 1 forming eight cavities 12 extending inward to the center of the solid . this folding operation is of great importance for this document , since it explains the structure of the building block . furthermore , we have to correct the meaning of the terms “ small square ” and “ big square ”. the small square 10 will continue being the one with the measurements a = d /√ 2 and the diagonal d = ⅛c . notwithstanding , the big square 11 has new measurements a = d and d = 2a . to avoid confusions with the descriptions of the copending application , the measures of the face of the cube herein will be aa = 2d and the diagonal dd = 4a . this is seen in fig2 , where the corners of the big squares 11 are called v and between these corners we find j . the four points j form the “ small square ” 10 , corresponding to the upper and lower surfaces 7 & amp ; 8 of the subunits 4 , inscribed inside the big square 11 . one upper or lower surface plus four angular faces along the sides form a big square 11 . with the diagonals of the small square 10 you measure the sides of the big square 11 and with the sides you measure the diagonals . we will call w the central point of the path ( a ) of the small square . the vertices v appear at the white whole square diagonal crossing in the cube , while in the sphere 1 the vertices v correspond to the apexes of the triangles 5 and define either a point towards the interior of the sphere 1 or the corner points of the upper surface 7 of the subunits 4 . these vertices v together with the angular faces 6 define the cavities 12 at y on the spherical block 1 . a cube can also serve as an imaginary frame to guide the position of nine spherical blocks 1 to form a cubical structure . take a cube with a side aa = 18 . each of the eight corners is the nucleus of a spherical block 1 with radius r = 8 . 91 ≈ 9 . it is impossible to place a ninth sphere 13 with a similar radius in the nucleus of the cube , unless you allow an overlap among the spheres . the calculation for that overlap is as follows : the space diagonal of the cube measures √( dd ″+ aa ″)≈ 31 . 2 ; the corner radiuses and the double radius of the ninth sphere add up to ≈ 35 . 6 and the overlap is ≈ 4 . 44 . if we are able to build a sphere with a gearing or connection of ½overlap ≈ 2 . 22 we can introduce the ninth sphere 13 and so connect the space not only through the axes 14 ( x , y , z ) but also through the 4 diagonal axes 15 or space diagonals as shown in fig4 . since the ninth sphere 13 is in the center , the connection is given with the eight spheres around it . in order to maintain the symmetry , the gearing or connection must be located in the centers y of the eight octants corresponding to the cavities 12 . we point out that in reality all the spheres can be a ninth sphere , depending on where the borders that outline it are located . as should now be clear , the starting point for the spherical building block 1 of the present invention is the square . the union of two squares forms a pair or subunit 4 and the union of eighteen pairs or subunits 4 in three intersecting rings 9 forms spherical building block 1 that allows for the joining of multiple blocks 1 in the seven directions , three for the x , y , z axes 14 and in four space diagonal directions 15 . the basic component of the block 1 is the pair or subunit 4 , made up by the union of two big squares 11 , with m as the exterior surface 7 and f as the interior surface 8 . m and f are joined in a complementary way as shown in fig3 a . starting at any point : j of m and v of f , they are joined at the sides until the next intersection v of m with j of f and continuing that way around the periphery until arriving to the starting point . at the end you obtain eight j - v unions . at the moment of the folding , the big square 11 of one of the pairs forms a plane or flat surface with the size of the small square 10 and the leftovers at the corners are folded in the direction of its pair &# 39 ; s corners to form the angular faces 6 . these leftovers or angular faces 6 are the triangles jvj 5 and are interdigitated between the pairs f and m of the subunit 4 to close the existing space between the two planes , the one of f in the interior or flat lower surface 8 and the one of m in the exterior or spherical upper surface 7 as shown in fig3 a and b . we now describe an imaginary frame or support that serves as guide to locate each of the pairs or subunits 4 . starting with a cube with sides 12 and diagonal 17 , the numbers are rounded to avoid dealing with square roots , graphing of the cube &# 39 ; s faces is described as five squares and four rectangles : one central square ( 5 ), four corner squares ( 3 . 5 ) and in the borders of the central square , four rectangles ( 5 × 3 . 5 ). cut the twelve borders of the cube at the diagonal of the squares ( 3 . 5 ) and the new face measures 5 like the central square . the perimeter c1 is no longer 4 × 12 = 48 but 8 × 5 = 40 . finally a cut in the corners of the cube forms eight equilateral triangles with side 5 . the resulting figure is a rhombicuboctahedron composed of eighteen squares and eight equilateral triangles , all with sides a = d √ 2 , and represents the eighteen bases on which to sit the pairs or subunits 4 on the side f or lower flat surface 8 and is nothing more than a visual guide since the pairs are sustained among themselves . if we cut over any circumference c1 , the support appears like a regular octagon with sides 5 . on the outside we outline an octagon with sides d = 7 whose circumference equals c1 . the octagon has two radiuses , the subscribed and the circumscribed . the radius that the outer octagon d = 7 must adopt to reach the lower flat surface of f is the radius for a circle c1 = 8d = 56 . in a plane view , the diagonal path of the big square that appears over the support is wxw = 5 or “ a ” and it must not be mistaken with jwj with a similar measurement 5 or “ a ”. the total diagonal path of the lateral view f cut is d = 2a , that is equal to the sum of 2 . 5 + 5 + 2 . 5 or ½a + a + ½a = 2a . the leftovers of f , called wv = ½a = 2 . 5 , and which form the angular faces 6 go up through the line of the radius seeking the encounter with m between the corresponding angular faces 6 thereof , but they cannot go farther since their job is to maintain the 45 degree angle that allows for the formation of the subunit 4 . it is m which must make an effort to reach f to close the openings . when m finds f the periphery is closed , the surface 7 of m becomes semispherical and the subunit 4 is formed as shown in fig3 . at the end , the important thing is that with eighteen pairs or subunits 4 you can form the spherical building block 1 and in it eight gearings or connections with the exact need measurement for the overlap that allows for the introduction of the ninth sphere 13 and the view of the seven paths . we now present a practical system to describe the magnetic flow and to locate the magnets easily in the different octants . we make reference to the cube in order to facilitate the location , but we are talking about a spherical building block of the present invention . we number each face in accordance with the numbers of a game dice : 1 on the front , 2 top left , 3 top right , 4 bottom left , 5 bottom right and 6 on the back . the opposing faces are therefore 3 & amp ; 4 , 2 & amp ; 5 and 1 & amp ; 6 . the twelve borders or edges of the die are 2 - 3 , 2 - 5 , 4 - 5 , 2 - 4 , 1 - 2 , 2 - 6 , 5 - 6 , 1 - 5 , 1 - 3 , 3 - 6 , 4 - 6 , and 1 - 4 . the octants corresponding to the corners y are determined by the union of three faces and are represented with respect to the spherical building block 1 in fig6 . each four corner group is separated among its members by dd and from the members of the other group by aa . this is reasonable since the distance between similar charges must be greater than the distance between contrary charges . in the sphere this difference is balanced , as long as we take into account the width of the energy , even though there is always a fixed difference to promote the flow without having a disorder . the gearing or connection among spheres takes place at points y which correspond to the eight triangular cavities 12 formed between the three intersecting rings of subunits and are the spherical equivalent of the corners of the cube . fig6 shows one such octant or corner with the triangular cavity 12 defined by the edges of three adjacent subunits 4 , one from each ring 9 and corresponding to the z subunits of those rings . midway along each side of the triangular cavity 12 are free corner points 16 of the upper surface 7 of the z subunits which correspond to the corners j of the small square 10 forming the upper surface 7 of the subunit 4 . when two spherical building blocks 1 are brought together to create a larger structure , the free corner points 16 fit into corresponding apexes of the triangular cavity 12 , which correspond to the corners v of the big square 11 , to provide a gearing or intermeshing between adjacent spherical building blocks which serves to hold the adjacent blocks in registry with each other . although the gearing or intermeshing between adjacent spherical building blocks 1 holds the blocks in registry with each other , it is not sufficient to hold the individual blocks 1 together so as to permit a structure to be constructed without that structure simply falling apart due to gravity . whereas many means could be employed to secure a plurality of the spherical building blocks 1 together to form a structure , including mechanical connectors , adhesive , electrostatic attraction , or the like , a simple and readily engagable and releasable connection means is preferred . for this purpose it has been found that magnetic attraction is preferred . indeed , the construction of the spherical building block 1 from three intersecting rings 9 facilitates the use of magnets as a releasable connecting means between adjacent spherical building blocks . for the case of the toy building block , in an initial stage the creation of the magnetic flow is not necessary but only the right location of the polarities of the magnets in the centers y of the cavities 12 . thus , the gearing or connection of multiple spherical building blocks of the present invention by the intermeshing of the free corner points 16 takes place at the centers y corresponding to the cavities 12 in which the poles of magnets corresponding to the space diagonals 15 are located . the combination of magnetic attraction and the gearing or intermeshing of adjacent spherical blocks provides a more positive engagement than would be possible with purely spherical building blocks not having the subunit ring structure of the present invention . furthermore , since the intersecting ring structure of the spherical building block results in eight cavities 12 , as opposite pairs , each pair can represent a north and a south magnetic pole . preferably , the magnetic poles are fixed at their respective locations . however it is conceivable within the present invention to include versions with the magnets held within the cavities by flexible means , such as springs , to allow a degree of flexibility and movement of the union between adjacent spherical building blocks 1 thereby providing some resilience to a structure constructed from the blocks . the above description explains the derivation of the spherical building block of the present invention from a cube and a plurality of squares defining the faces of the cube , the subunits of the building block corresponding to those squares . however , it will be readily appreciated that the subunits 4 may be individually molded according to the dimensions and angular relationships set forth and assembled to form the spherical building block 1 made up of three intersecting rings x , y and z . furthermore , the size of the building block can be scaled to any requirement since the proportions of the subunits 4 are constant . in a still further alternative manufacturing method shown in fig6 , the spherical building block 1 may be assembled from six molded faces 16 each comprising a whole subunit 4 at the center with a half subunit 17 on each side forming a module having the shape similar to that of a maltese cross , fig7 . the molded faces 16 are united at each arm of the cross structure to form the spherical building block 1 with magnets located at each cavity 12 defined by the corners of three adjoining molded faces 16 . using the building block 1 of the present invention it is possible to assemble different and complex structures as represented by fig5 providing a flexibility in the creation of figures not possible with conventional building blocks . while the invention has been described with respect to certain specific embodiments , it will be appreciated that many modifications and changes may be made by those skilled in the art without departing from the spirit of the invention . it is intended , therefore , that all such modifications and changes are within the true spirit and scope of the invention as recited in the following claims .