as described in detail below , various embodiments of the invention include a multi - dimensional puzzle . the invention has significant benefits across a broad spectrum of endeavors . it is the applicant &# 39 ; s intent that this specification and the claims appended hereto be accorded a breadth in keeping with the scope and spirit of the invention being disclosed despite what might appear to be limiting language imposed by the requirements of referring to the specific examples disclosed . fig1 a and 1b depict non - planar forms 2 , and fig2 a and 2b depict planar forms 12 . the non - planar form 2 of fig1 a and the planar form 12 of fig2 a may combine to form a spatial assembly according to one embodiment of the invention . further , the non - planar form 2 of fig1 b and the planar form 12 of fig2 b may combine to form a spatial assembly according to another embodiment of the invention . the non - planar forms of fig1 a and 1b have a plurality of protrusions 4 , three protrusions in this embodiment , extending in a first direction wherein at least one recess 6 is disposed between the protrusions 4 . another plurality of protrusions 8 , three protrusions in this embodiment , extends in a second direction wherein at least one recess 10 is disposed between the protrusions 8 . the first and second directions are perpendicular , and the two pluralities of protrusions 4 , 8 lie in different planes , i . e ., the two pluralities of protrusions 4 , 8 do not lie in a common plane . the planar forms of fig2 a and 2b also have a plurality of protrusions 14 , three protrusions in this embodiment , extending in a first direction wherein at least one recess 16 is disposed between the protrusions 14 . a second plurality of protrusions 18 , three protrusions in this embodiment , extends in a second direction wherein at least one recess 20 is disposed between the protrusions 18 . in addition , the protrusions of the second plurality of protrusions 18 do not lie adjacent to one another . as depicted in fig2 a and 2b , two protrusions lie on one side of the first plurality of protrusions 14 , and one protrusion lies on the other side of the first plurality of protrusions 14 . the first and second directions are perpendicular , and the two pluralities of protrusions 14 , 18 lie in a common plane . the protrusions 4 , 8 , 14 , 18 of the forms 2 , 12 in fig1 a and 2a have the same dimensions . the protrusions 4 , 8 , 14 , 18 have an overall length l , a height h which is smaller than length l , and a width w which is smaller than height h . in the embodiments in fig1 a and 2 a , the height h is l / 2 , and the width w is l / 6 . similarly , the protrusions 4 , 8 , 14 , 18 in fig1 b and 2b have the same dimensions . the protrusions 4 , 8 , 14 , 18 have an overall length l , a height h which is equal to length l , and a width w that is smaller than length l and height h . in this embodiment , width w is l / 6 , or alternatively h / 6 . it will be appreciated that the relative sizing between l , h , and w may be any combination discussed elsewhere herein . fig3 a - 3c , show the various stages of creating a spatial assembly from non - planar forms and planar forms . fig3 a shows an assembly of eight non - planar forms 2 . the four non - planar forms 2 on top have alternating orientations . similarly , the four non - planar forms 2 on bottom also have alternating orientations . fig3 b shows an assembly of eight planar forms 12 . the four planar forms 12 on top have alternating orientations . similarly , the four planar forms 12 on bottom also have alternating orientations . fig3 c shows the eight non - planar forms 2 and the eight planar forms 12 assembled into a spatial assembly 22 , which in this embodiment is a cube . fig3 c also shows that the non - planar forms 2 and the planar forms 12 may be comprised of different materials or materials with different opacities . one of the forms 2 , 12 may represent negative space , and the other form 2 , 12 may represent positive space . fig4 shows one stage of assembling the spatial assembly 22 wherein all of the forms 2 , 12 are only partially interconnected , and thus , how the forms 2 , 12 selectively interconnect with one another . as shown , the protrusions of a planar form 12 slide into the recesses of a non - planar form 2 , and vice versa . in this embodiment , all of the non - planar forms 2 are interconnected to each other to create a composite form . fig5 shows a later stage of assembling the spatial assembly 22 wherein half of the spatial assembly 22 is assembled such that the non - planar forms 2 are interconnected and wherein the planar forms 12 are in the process of selectively interconnecting to the non - planar forms 2 . fig6 shows the spatial assembly 22 completely assembled . once the stages of assembly as depicted by fig4 and 5 are successfully completed , the forms 2 , 12 create a spatial assembly 22 . as shown , the protrusions and recesses of the planar forms 12 are selectively interconnected with the recesses and the protrusions of the non - planar forms 2 such that there is no space between the two forms . fig7 a - 7c show an embodiment of the invention where the forms comprise protrusions of differing shapes and lengths such that planar and non - planar forms assemble to create a cylindrical spatial assembly 44 . the non - planar form 24 of fig7 a has a plurality of protrusions 26 , three protrusions in this embodiment , extending in a first direction wherein at least one recess 28 is disposed between the protrusions 26 . another plurality of protrusions 30 , three protrusions in this embodiment , extends in a second direction wherein at least one recess 32 is disposed between the protrusions 30 . the first and second directions are perpendicular , and the two pluralities of protrusions 26 , 30 lie in different planes , i . e ., the two pluralities of protrusions 26 , 30 do not lie in a common plane . the planar form 34 of fig7 b also has a plurality of protrusions 40 , three protrusions in this embodiment , extending in a first direction wherein at least one recess 42 is disposed between the protrusions 40 . a second plurality of protrusions 36 , three protrusions in this embodiment , extends in a second direction wherein at least one recess 38 is disposed between the protrusions 36 . in addition , the protrusions of the second plurality of protrusions 36 do not lie adjacent to one another . as depicted in fig7 b , two protrusions lie on one side of the first plurality of protrusions 40 , and one protrusion lies on the other side of the first plurality of protrusions 40 . the first and second directions are perpendicular , and the two pluralities of protrusions 36 , 40 lie in a common plane . eight planar forms 34 and eight non - planar forms 24 combine to form the cylindrical spatial assembly 44 shown in fig7 c . fig8 a - 8c show an embodiment of the invention where the forms comprise protrusions of differing shapes and lengths such that planar and non - planar forms assemble to create a spherical spatial assembly 66 . the non - planar form 46 of fig8 a has a plurality of protrusions 48 , three protrusions in this embodiment , extending in a first direction wherein at least one recess 50 is disposed between the protrusions 48 . another plurality of protrusions 52 , three protrusions in this embodiment , extends in a second direction wherein at least one recess 54 is disposed between the protrusions 52 . the first and second directions are perpendicular , and the two pluralities of protrusions 48 , 52 lie in different planes , i . e ., the two pluralities of protrusions 48 , 52 do not lie in a common plane . the planar form 56 of fig8 b also has a plurality of protrusions 62 , three protrusions in this embodiment , extending in a first direction wherein at least one recess 64 is disposed between the protrusions 62 . a second plurality of protrusions 58 , three protrusions in this embodiment , extends in a second direction wherein at least one recess 60 is disposed between the protrusions 58 . in addition , the protrusions of the second plurality of protrusions 58 do not lie adjacent to one another . as depicted in fig8 b , two protrusions lie on one side of the first plurality of protrusions 62 , and one protrusion lies on the other side of the first plurality of protrusions 62 . the first and second directions are perpendicular , and the two pluralities of protrusions 58 , 62 lie in a common plane . eight planar forms 56 and eight non - planar forms 46 combine to form the cylindrical spatial assembly 66 shown in fig8 c . fig9 a - 9c show various combinations of different types of planar and non - planar forms . fig9 a shows a mixed spatial assembly 68 that combines non - planar forms for a spherical spatial assembly with planar forms for a cube spatial assembly . fig9 b shows a mixed spatial assembly 70 that combines non - planar forms for a cube assembly with planar forms for a spherical assembly . fig9 c shows a mixed spatial assembly 72 where half of the spatial assembly is a sphere and the other half of the spatial assembly is a cube . it will be appreciated that any combination planar forms , non - planar forms , or any other type of forms may be used to create any number of shapes or structures . in this specification , the phrases “ at least one ”, “ one or more ”, and “ and / or ”, as used herein , are open - ended expressions that are both conjunctive and disjunctive in operation . for example , each of the expressions “ at least one of a , b , and c ”, “ at least one of a , b , or c ”, “ one or more of a , b , and c ”, “ one or more of a , b , or c ,” and “ a , b , and / or c ” means a alone , b alone , c alone , a and b together , a and c together , b and c together , or a , b , and c together . unless otherwise indicated , all numbers expressing quantities , dimensions , conditions , and so forth used in the specification , drawings , and claims are to be understood as being modified in all instances by the term “ about .” the term “ a ” or “ an ” entity , as used herein , refers to one or more of that entity . as such , the terms “ a ” ( or “ an ”), “ one or more ” and “ at least one ” can be used interchangeably herein . the use of “ including ,” “ comprising ,” or “ having ,” and variations thereof , is meant to encompass the items listed thereafter and equivalents thereof as well as additional items . accordingly , the terms “ including ,” “ comprising ,” or “ having ” and variations thereof can be used interchangeably herein . it shall be understood that the term “ means ” as used herein shall be given its broadest possible interpretation in accordance with 35 u . s . c ., section 112 ( f ). accordingly , a claim incorporating the term “ means ” shall cover all structures , materials , or acts set forth herein , and all of the equivalents thereof . further , the structures , materials , or acts , and the equivalents thereof , shall include all those described in the summary of the invention , brief description of the drawings , detailed description , abstract , and claims themselves . the foregoing description of the invention has been presented for illustration and description purposes . however , the description is not intended to limit the invention to only the forms disclosed herein . in the foregoing detailed description for example , various features of the invention are grouped together in one or more embodiments for the purpose of streamlining the disclosure . this method of disclosure is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim . rather , as the following claims reflect , inventive aspects lie in less than all features of a single foregoing disclosed embodiment . thus , the following claims are hereby incorporated into this detailed description , with each claim standing on its own as a separate preferred embodiment of the invention . consequently , variations and modifications commensurate with the above teachings and skill and knowledge of the relevant art are within the scope of the invention . the embodiments described herein above are further intended to explain best modes of practicing the invention and to enable others skilled in the art to utilize the invention in such a manner , or include other embodiments with various modifications as required by the particular application ( s ) or use ( s ) of the invention . thus , it is intended that the claims be construed to include alternative embodiments to the extent permitted by the prior art .
the invention generally relates to multi - dimensional puzzles for teaching , entertainment , and construction . one embodiment of the invention comprises two forms , one planar and one non - planar , which comprise a plurality of protrusions and recesses . these forms may be assembled by selectively interconnecting the various protrusions and recesses to create multi - dimensional shapes such as a cube , cylinder , and sphere among many other possibilities .