You are an expert at summarizing long articles. Proceed to summarize the following text:

You are an expert at summarizing long articles. Proceed to summarize the following text: 
FIELD OF THE INVENTION 
       [0001]    The present invention relates to construction or building blocks having complementary-shaped surfaces to restrain relative movement. 
       BACKGROUND TO THE INVENTION 
       [0002]    The use of traditional bricks-and-mortar construction presents some well-known limitations in building. These limitations include the need for skilled labour to achieve an even, square result; limitations in the speed at which a structure can be erected due, for instance, to the requirement for mortar to cure; and limitations in the compressive load carrying ability of the structure due to the variation in stiffness between bricks and mortar. 
         [0003]    The use of pre-cast concrete panels has become more common in recent years, in an attempt to ameliorate some of these limitations. The use of such panels has its own limitations, including difficulties in adapting panels to a particular site, and the need for mechanised equipment during movement and installation of the panels. 
         [0004]    In another alternative to traditional bricks-and-mortar construction, interlocking building blocks have been used in some applications. One example of this is the Haener block, shown in U.S. Pat. No 3,888,060. The Haener block has interlocking tongue-and-groove style projections between adjacent blocks. Also available are building blocks having projections on one side and corresponding recesses on an opposing side. An example is the Habegger block, shown in U.S. Pat. No. 4,1124,961. This style of block has complementary upper and lower surfaces, with projections on a lower surface which locate within hollows on an upper surface. 
         [0005]    The advantage of interlocking building blocks is that they are largely self-locating, and do not require mortar, thus allowing for the quick erection of structures by largely unskilled labour. 
         [0006]    It is also known to use interlocking blocks in the laying of segmental block paving. Traditional paving methods rely on frictional engagement between adjacent paving bricks to prevent movement of the paving under load. The effectiveness of this is reliant on many factors, including the paver shape, the laying pattern, and the properties of the joint sand and the bedding sand. These factors are difficult to quantify and thus control. 
         [0007]    In an attempt to ameliorate these problems, systems of interlocking blocks, such as those described in U.S. Pat. No. 6,988,847, have been employed as paving blocks. 
         [0008]    All of the interlocking block systems described above have been designed to suit a specific construction purpose. It is considered desirable to create a construction block design which can be used for both building and paving, as well as other applications. The present invention seeks to meet this desire. 
         [0009]    The present invention employs the principle of topological interlocking, where surfaces of adjacent blocks are of complementary shape. An example of this principle can be found in GB 1,533,980, which proposes building blocks having sides which follow a sinusoidal curve. 
         [0010]    A significant limitation of this design is that unless adjacent blocks are perfectly aligned, significant stress concentrations can occur at the resulting point or line loading points. The design also requires a high degree of accuracy in manufacture. The present invention proposes an alternative construction block design in light of the difficulties of the prior art. 
       SUMMARY OF THE INVENTION 
       [0011]    According to one aspect of the present invention there is provided a construction block having a first end and a second end; each of the first end and the second end having a plurality of substantially planar bearing surfaces, at least two of the bearing surfaces being relatively disposed at an obtuse angle, wherein an engaging portion of the first end of a first block is complementary in shape to an engaging portion of the second end of a second block, and whereby the first end of the block includes at least one outermost bearing surface furthest from the second end and at least one innermost bearing surface closest to the second end, both the innermost and outermost bearing surfaces being adjacent a periphery of the first end. 
         [0012]    It is preferred that the block has a length which is twice its width, and that the engaging portions can be engaged when the first block is offset relative to the second block by half the block&#39;s length. It will be appreciated that in this arrangement the engaging portions are substantially square, and that each end of the block has two engaging portions located side-by-side. 
         [0013]    It is further preferred that each engaging portion is symmetrical about a diagonal, such that the first block can be arranged to be perpendicular to the second block with the engaging portions in engagement. 
         [0014]    In a preferred embodiment of the invention, some of the bearing surfaces are substantially perpendicular to side walls of the block. These bearing surfaces, which are horizontal when the side walls are vertical, may be located at two heights, with angled bearing surfaces extending between horizontal surfaces at different heights. It will be appreciated that when the side walls are vertical, and the first end located at the top of the block, the highest horizontal bearing surface is the outermost bearing surface, and the lowest horizontal bearing surface is the innermost bearing surface. It is preferred that each engaging portion has two highest horizontal bearing surfaces, located at diagonally opposed corners of the engaging portion; and two lowest horizontal bearing surfaces located at the other corners of the engaging portion. The horizontal bearing surfaces may each be square, with a side length approximately equal to one quarter of the block width. 
         [0015]    It is also preferred that each engaging portion has a point at which at least four bearing surfaces meet. This point may be centrally located, and may represent a point of inflexion. 
         [0016]    Adjoining engagement portions are preferably reflected about the middle of a block, such that the bearing surfaces located along the middle of a block end are substantially continuous between the two engaging portions. 
         [0017]    It is preferred that the block be symmetrical about a plane of symmetry located midway between the first end and the second end, perpendicular to the side walls. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    It will be convenient to further describe the invention with reference to preferred embodiments of the construction block of the present invention. Other embodiments are possible, and consequently the particularity of the following discussion is not to be understood as superseding the generality of the preceding description of the invention. In the drawings: 
           [0019]      FIG. 1  is a perspective of a construction block in accordance with the present invention; 
           [0020]      FIG. 2  is a top plan view of the construction block of  FIG. 1 ; 
           [0021]      FIG. 3  is a perspective of a corner of a building constructed with the blocks of  FIG. 1 ; 
           [0022]      FIG. 4  is a perspective of a portion of a column constructed with the blocks of  FIG. 1 ; 
           [0023]      FIG. 5(   a ) is a perspective of a portion of paving using the blocks of  FIG. 1 ; 
           [0024]      FIG. 5(   b ) is a perspective of alternative paving using the blocks of  FIG. 1 ; 
           [0025]      FIG. 6  is a perspective of an alternative construction block in accordance with the present invention; 
           [0026]      FIG. 7  is a perspective of a further alternative construction block in accordance with the present invention; 
           [0027]      FIG. 8  is a perspective of a portion of a double-leaf wall formed using the construction blocks of  FIG. 7 ; 
           [0028]      FIG. 9  is a perspective of a portion of a cavity wall formed using the construction blocks of  FIG. 7 ; 
           [0029]      FIG. 10  is a perspective of a construction block formed according to similar principles to that of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0030]    Referring to the Figures,  FIG. 1  shows a construction block  10  having a first end  12 , a second end  14 , two first side walls  16  and two second side walls  18 . When the block  10  is held in the position of  FIG. 1 , the first and second side walls  16 ,  18  are all vertical, planar surfaces. 
         [0031]    The first side walls  16  are twice the width of the second side walls  18 , meaning that if a horizontal cross section were taken through centre of the block  10  the result would be a rectangle with a length twice its width. 
         [0032]    The first end  12  has a plurality of bearing surfaces, including horizontal bearing surfaces and angled bearing surfaces as will be described in greater detail below. The angled bearing surfaces each make an obtuse angle with respect to the horizontal bearing surfaces. In some cases the angled bearing surfaces also make an obtuse angle with respect to each other. 
         [0033]    For the purposes of description, the first end  12  can be divided into two engaging portions  20 , by drawing an imaginary dividing line  22  parallel to the second side walls  18 , mid-way through the first side walls  16 . Each of the engaging portions  20  is square when viewed from above. 
         [0034]    Each of the engaging portions  20  has four horizontal bearing surfaces: a first high horizontal bearing surface  24  located at an outer corner of the first end  12 ; a second high horizontal bearing surface  26  located at a diagonally opposed corner of the engaging portion  20 , along the dividing line  22 , and at the same height as the first high horizontal bearing surface  24 ; a first low horizontal bearing surface  28  located at the other outer corner of the first end  12 ; and a second low horizontal bearing surface  30  diagonally opposed to the first low horizontal bearing surface  28 , and at the same height as the first low horizontal bearing surface  28 . Each of the four horizontal bearing surfaces is square, with a side length equal to one quarter of the width of the block  10 . 
         [0035]    The high horizontal bearing surfaces  24 ,  26  can be described as outermost bearing surfaces of the first end  12 . The low horizontal bearing surfaces  28 ,  30  can be described as innermost bearing surfaces of the first end  12 . Each of the outermost and innermost bearing surfaces is located about a periphery  31  of the first end  12 . Each of the engaging portions  20  has four planar angled bearing surfaces. When viewed from above, as shown in  FIG. 2 , each of these surfaces lies within a quarter of the engaging portion  20  defined by diagonal lines. 
         [0036]    The first angled surface  32  lies in the quarter defined by the first high horizontal bearing surface  24  and the second low horizontal bearing surface  30 . The angle α between the first high horizontal bearing surface  24  and the first angled bearing surface  32  is a function of the difference in heights Δh between the horizontal bearing surfaces, with tan(180°−αa)=Δh/(w/2), w being the width of the block  10 . 
         [0037]    The second angled surface  34  lies in the quarter defined by the first high horizontal bearing surface  24  and the first low horizontal bearing surface  28 . The third angled surface  36  lies in the quarter defined by the second high horizontal bearing surface  26  and the first low horizontal bearing surface  28 . The fourth angled surface  38  lies in the quarter defined by the second high horizontal bearing surface  26  and the second low horizontal bearing surface  30 . 
         [0038]    Adjacent angled bearing surfaces form a ridge  33  along the diagonal between the high horizontal bearing surfaces  24 ,  26 , and a valley  35  along the diagonal between the low horizontal bearing surfaces  28 ,  30 . The centre  37  of the engaging portion  20  is a point of inflection. 
         [0039]    The arrangement of the bearing surfaces of the two engaging portions  20  is mirror-imaged about the dividing line  22 . The respective second high horizontal bearing surfaces  26  of the two engaging portions  20  are continuous, as are the respective second low horizontal bearing surfaces  30  and the respective fourth angled surfaces  38 . 
         [0040]    The second end  14  is formed identically to the first end  12 , such that if the block  10  were inverted it would appear identical. The arrangement of high and low bearing surfaces on the second end  14  are such that the first side walls  16  of the block  10  are both symmetrical about two lines of symmetry: a vertical line (aligned with the dividing line  22 ) and a horizontal line on symmetry. In other words, if the average height of the block is h, the height of the block beneath the high horizontal bearing surfaces  24 ,  26  is h+Δh, whereas the height beneath the low horizontal bearing surfaces  28 ,  30  is h−Δh. 
         [0041]    The first end  12  of the block  10  is thus not complementary in shape to the second end  14  of the block  10 . On the other hand, each of the engaging portions  20  of the first end  12  of the block  10  is complementary in shape to the other of the engaging portions of the second end  14  of the block  10 . In other words, the first end  12  of the block  10  is complementary to the second end  14  when offset by half the length of the block  10 . 
         [0042]    It will also be apparent that the block  10  is symmetrical about a horizontal plane of symmetry. 
         [0043]    The usefulness of this arrangement in construction can be seen in  FIG. 3 , which shows a corner of a building  40  constructed with construction blocks  10 . It will be seen that successive courses of blocks  10  are offset by half the length of a single block  10 , creating a fully interlocked structure. 
         [0044]    In addition, it can be seen that as each engaging portion is symmetrical about each of its diagonal, respective engaging portions  20  of the first end  12  and second end  14  are complementary when relatively rotated by 90°. The corner shown in  FIG. 3  can therefore be created without the need for other types of block. 
         [0045]    Other useful arrangements will be apparent.  FIG. 4  shows a column  42  built entirely from interlocking blocks  10 .  FIGS. 5(   a ) and  5 ( b ) show two possible arrangements of paving  44  using interlocking blocks  10 . 
         [0046]    It will be appreciated that when correctly constructed each of the bearing faces will abut a bearing face of another block, allowing load to be distributed across the end of the block. Where adjacent blocks are not properly aligned, not all of the bearing faces will be in a position to transfer load. Due to the use of planar surfaces, however, at least one pair of surfaces will be abutting, and able to distribute load across the abutting surface area. This is in contrast to curved topological surfaces, where misalignment generally results in a point load. 
         [0047]    Other embodiments of the present invention provide further advantages.  FIG. 6  shows an alternative construction block  50  where the edges between adjoining bearing surfaces have been rounded to assist in construction. 
         [0048]      FIG. 7  shows a further alternative construction block  60  having horizontal grooves  62  extending midway along each angled bearing surface into which horizontal rebars  66  can be received, and vertical slots  64  though the centre of each engaging portion  20  through which vertical rebars  68  can be received. These versions allow for stronger structures to be built using the construction blocks. Examples include double-leaf walls  70  such as that of  FIG. 8  and cavity walls  80  such as that of  FIG. 9 . 
         [0049]    The construction block shown in  FIGS. 1 to 9  is a specific example of a more general style of block. Such a block is characterised by having an upper surface defined according to the equation: 
         [0000]        z   1 ( x, y )=Δ h φ( x )φ( y )+ h  
 
         [0000]    and a lower surface defined according to the equation: 
         [0000]        z   2 ( x, y )=Δ h φ( x +α)φ− h  
 
         [0000]    where h is the average height of the block above its midline; Δh is the difference between average height and top height of the block; α is the block width (so 2α is block length) and φ(x) is any function satisfying the following conditions of symmetry, periodicity, and boundary: 
         [0000]      φ( x )=φ(− x ); φ( x )=φ( x +2α); φ(0)=1; φ(α)=−1; φ′(0)=φ′(α)=0.
 
         [0050]    Expressed in these terms, the block of  FIG. 1  has an upper surface defined as follows: 
         [0000]    
       
         
           
             
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         [0051]      FIG. 10  shows an alternative construction block  90  which employs a curvilinear surface defined according to the equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     z 
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                         , 
                         y 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         A 
                         ′ 
                       
                        
                       
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       r 
                                       2 
                                     
                                     - 
                                     
                                       
                                         ( 
                                         
                                           x 
                                           - 
                                           
                                             
                                               B 
                                               ′ 
                                             
                                              
                                             a 
                                           
                                         
                                         ) 
                                       
                                       2 
                                     
                                   
                                 
                                 - 
                                 r 
                                 + 
                                 
                                   0.5 
                                    
                                   
                                       
                                   
                                    
                                   Δ 
                                    
                                   
                                       
                                   
                                    
                                   h 
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               ( 
                               
                                 
                                   
                                     
                                       r 
                                       2 
                                     
                                     - 
                                     
                                       
                                         ( 
                                         
                                           y 
                                           - 
                                           
                                             
                                               C 
                                               ′ 
                                             
                                              
                                             a 
                                           
                                         
                                         ) 
                                       
                                       2 
                                     
                                   
                                 
                                 - 
                                 r 
                                 + 
                                 
                                   0.5 
                                    
                                   
                                       
                                   
                                    
                                   Δ 
                                    
                                   
                                       
                                   
                                    
                                   h 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       0.5 
                        
                       
                           
                       
                        
                       Δ 
                        
                       
                           
                       
                        
                       h 
                     
                   
                 
               
               
                 □ 
               
             
           
         
       
     
         [0000]    where 
         [0000]        A′= 1 for 0≦ x ≦0.5 a, 1.5 a≦x≦ 2 a  and 0 ≦y≦ 0.5 a,  0.5 a≦x≦a.  5 a  and 0.5 a≦y≦a;  
 
         [0000]        A′= 1 for 0.5 a≦x≦ 1.5 a  and 0≦ y≦ 0.5 a,  0≦ x≦ 0.5 a, 1.5 a≦x≦ 2 a  and 0.5 a≦y≦a;  
 
         [0000]        B′= 0 for 0≦ x≦ 0.5 a  and 0≦ y&lt;a;  
 
         [0000]        B′= 1 for 0.5 a≦x≦ 1.5 a  and 0≦ y≦a;  
 
         [0000]        B′= 2 for 1.5 a≦x≦ 2 a  and 0≦ y≦a;  
 
         [0000]        C′= 0 for 0≦ x≦ 2 a  and 0≦ y≦ 0.5 a ; and
 
         [0000]        C′= 1 for 0≦ x≦ 2 a  and 0.5 a≦y≦a;  
 
         [0052]    This block has many of the properties of the construction block of  FIGS. 1 to 9 , with the principle difference being the propensity for point loads when successive blocks are misaligned. 
         [0053]    Modifications and variations as would be apparent to a skilled addressee are deemed to be within the scope of the present invention.

Summary:
An interlocking construction block has opposed ends each having a plurality of substantially planar bearing surfaces. The planar surfaces include perpendicular surfaces joined by surfaces at obtuse angles. The block is arranged to be complementary to other blocks in several different configurations.