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Six-axis star

The configuration of sticks in these structures is the same as the configuration of wires in some of John’s earlier patented work with symmetrically joining beams.  The folding 6-axis and 4-axis bronze wire stars shown below were two of the many star structures he first started making and marketing in the mid 1960s.

Some more images of small wooden puzzles/boxes/sculptures:

Objects like these, in both 3” and 4” scale, as well as the bronze stars on which their design is based, are available for purchase by contacting us.  We work on commission and don’t keep much inventory.

Click here for a blog review from one of our customers.

Each wooden stick in the magnetic Tetraxis sculpture corresponds to one of the twelve wires in the Tetraxis star.

This can be illustrated by working backwards from the wooden version to the wire version.  Each stick is removed and replaced by a dowel.

Looking at the end of a wire or dowel, you can see that the shape of the space it passes through is an equilateral triangle.

bronze

Tetraxis star

SCALED UP

I constructed large versions of some of these puzzles in 2009.  Pictures here are from the Math Midway at the World Science Festival Street Fair in NYC.  The sticks are made out of a polyethylene foam, commonly used in packaging.  Each stick in the Tetraxis puzzle weighs about a pound.  Each of the Six-axis sticks weighs about half a pound.  The covers are Tyvek painted with fluid acrylics.

In 2009 we worked with an excellent company in Massachusetts called Datum3D to develop a more affordable 4” Tetraxis puzzle ($24.99) made of injection molded ABS plastic.  The toys were fabricated by a company in Xiamen, China, called Zhizi Mould.  We highly recommend both of these companies.  You can see more about this product at www.tetraxis.com.

The configuration of wires or rods in a Six-axis star can similarly be made so that each stick fills out the isosceles triangular space it passes through.  You can see the cross-section of the stick needs to be a 108°- 36°- 36° triangle:

In the 1990s John designed magnetic wooden stick versions of a few of his most basic star structures as a way to show the pattern in which the rods bypass one another around the core of the structure.  The intent was to make something easy to assemble.  The idea to use magnets in sticks this way came from seeing the use of magnets by our late friend Marvin Solit in his product RhomBlocks, which were wooden hexahedron blocks with ceramic magnets embedded in some of the faces.  Marvin was making these in the 1970s and 80s.  Later  RhomBlocks were manufactured by Stuart Quimby’s Design Science Toys.

Different kinds of woods can be mixed and matched to create lots of coloring patterns. This box that holds four sets of sticks was made by woodworker Tom Lensch for puzzle enthusiast John Rausch, who took the photos of it.

Shown below is an analogous 3-axis assembly in the shape of a rhombic triacontahedron.  It’s made of six blocks of wood that are sized just right to fit into the center of the wooden 6-axis puzzle.  The hollow space inside of that is a cube.  Click here for further description of the shape of each block.

Here is another set of sticks that’s analogous to those shown above.  This design comes from the 10-axis star, also one John used to make in the 1960s.  He calculated the angles of the space each wire passes through, which wasn’t quite as obvious as the others.  The two acute angles in the cross-section of this kite-shaped stick are both 60 degrees, the same as in a Tetraxis stick.  So in the corner where three sticks meet, you get the same look as the 3-fold corner in a Tetraxis sculpture.

Just as a 6-axis star can be interleaved with a 10-axis star to make a 16-axis star, the 6-axis sticks and the 10-axis sticks also can be put together to make a 16-axis sculpture.  Each of the 60 wooden sticks corresponds to one of the 60 wires in the bronze star.  I scaled these 10-axis sticks so that they fit perfectly around the 4” Six-axis sculpture, which surrounds the bronze star.

You can connect 90 Six-axis sticks inside out to surround the Ten-axis sculpture: