Radut's Cube is a three dimensional spatial puzzle modeled after the Burr Puzzle in design (spatial puzzles may be classified as jigsaws, burrs, or tangled). It was created by Dr. Florian Radut in 2002. The puzzle is advertised as, in terms of the special evolutionary tree that is spatial puzzles, the link between the soma cube and the popular Rubik's Bricks puzzles.
Radut's Cube is a simple game. Given 8 pieces of various geometry and color but identical volumes assemble one solid 2x2x2 cube. The catch is thus: the solved state must contain a checkerboard pattern of alternating light and dark material. Future explorations with the pieces give way to creating other symmetrical shapes while retaining this alternating scheme. The overall scheme is accomplished through a premediated piece construction.
Imagine four cubes of two different grained woods; Dr. Radut suggests cherry and beech, yours truly chose red maple and pine for a softer contrast. Once you have eight cubes, all of equal size, remove the same 1/8 scaled cube from each of your larger cubes. This is to say that for a 2" cube you would remove a cube 1"x1"x1". Afterwards, these small cubits would be attached (to cubes of the other color) in a manner to create seven unique geometries (one shape will be duplicated with a reverse color scheme). To explicate the piece creation process, envision that the cube is sitting on a diagonal in front of you, with the space formerly containing the removed cubit in the lower quadrant of the edge nearest to you. The dark cubes should have a light cubit attached to all three of the possible locations on the underside of the cube and one to the top of one cube in the right position (where the options are right, left, front, or back). The light cubes should have a dark cubit attached to the bottom back location (the bottom has locations only of back, left, and right - the bottom front is the removed space), as well as the following top locations: front, left, and back. What you should now have are seven geometrically unique pieces, with a duplicate of the piece with an extra cubit in the bottom back location. Solving the "cube" requires a symetrical shape with alternating colors. The two most frequent solutions would be the classical cube shape, as well as a row solution with two rows of four pieces which works well for potential storage.
Construction of the pieces necessary for the cube takes approximately three hours. You must obtain the wood you wish you use, plan a cut sheet (you'll be making six different cuts, some multiple times. don't forget about the kerf of the sawblade!), obtain a table saw and knowledge on how to safely use one, cut out the parts of your pieces, glue together the small cubes, obtain a motorized sander and knowledge on how to safely use one, sand the faces of the small cubes, glue the small cubits on in their appropriate places to form your eight pieces, and with fine sandpaper give a once over to all edges of your pieces.
With no machining tools, and no wish to glue 64 very small cubits together (remember, there are 8 pieces of 8 sub-quadrants each) I thought of a different method to construct my piece set. I procured two 1"x3" boards 24" in length. Since the width of these boards was actually 0.75" I knew my pieces (though not perfect cubes) would be of volume 1.5"x1.5"x1.5" and that the volume of my solved cube would be 27 cubic inches, or a very adult-hand-managable 3"x3"x3". This size may seem large to a child, but still should pose no handling difficulties. From each board I cut out eight 1.5"x1.5" squares, removing a 0.75"x0.75" square from every other one. By gluing one untouched square to one with a removed section, my base cublets were constructed. Four dark and four light 0.75"x0.75"x0.75" cubits later and my pieces were completed. I used carpentry grade wood glue (the bottle advertises 2-ton hold, but you can shear off misplaced cubits with a well aimed strike of a hammer) and held the pieces in small c-clamps for a half hour each to allow to set.
Directly after the final piece had dried, and a bit of showing off my new toy, I set to finding a solution. I would say it took about twenty minutes of fiddling to discover the logical rules to the puzzle (i.e. which pieces cannot be oriented which ways and why) and another five minutes to apply these rules and solve the puzzle. I will not be sharing what these rules are, because their realization is most of the fun of solving the puzzle. I had once set upon myself to solve a Rubik's Cube, and got along well enough with two discrete hints from a friend who had already done so. Two years and four mechanical puzzles later I was determined to not only solve a spatial puzzle, but to construct it as well for an immersive experience. Should any reader follow my construction notes, I would not wish to sully their experience with a "walkthrough" of one possible solution. I will, for those of you more insistent, provide a hint pipe-linked into the sources of this piece.