KO Sticks LLC | Geometric Structures by John and Jane Kostick
www.kosticks.com
  • Home
  • About Us
  • Stars
    • Star History
  • Woodwork
  • Magnetic Assemblies
    • Magnetic Assemblies
    • Quintetra
    • Triacontahedron Box
    • IPP32 entries
  • Tetraxis
    • Tetraxis Geometry
    • Tetraxis Toy >
      • Playdough
  • Perhaps of Interest
  • Purchasing
  • Contact Us

Magnetic Assemblies in Wood

Picture
Picture
Picture
photo: Dean Powell
Picture
Double Duals
Picture
Picture
Picture
Picture
Picture
Designed as interactive, wooden renditions of the cores of some of John's stars, these puzzle-like sculptures are handcrafted by Jane out of a wide variety of woods.   Embedded magnets help guide the sticks into position and enable the pieces to come apart and go back together easily in these highly symmetrical compositions.
Picture
Picture
Picture

Attractive to display and satisfying to play with, these are available for purchase by commission.  Prices range from about $100 to $800 and vary with wood selections.

Picture
Picture
Picture
Picture
Picture
Picture

      A good way to see some of these is in action:

Sixteen-Axis Star and Sticks

 
Picture
 


Picture



Tetraxis Star and Sticks

 
Picture

Click here for a plastic toy version of this.


Picture
Picture


Six-Axis Star and Sticks

 
Picture


Picture
There are so many ways to cut the ends of the sticks.
Picture
This video can also be viewed on Youtube.


To see the relationship between the stars and the stick sculptures, you can view the stars as kind of like skeletons of the wooden compositions, with each wire in a star corresponding to one stick of wood.  Each stick is made so that in cross-section it fills out the space it passes through.
Picture
Picture
Picture
Another way this can be illustrated is by working backwards from a wooden version to the wire version.  Here each stick is removed and replaced by a dowel.
Picture
Picture
Picture
Picture
Looking at the end of a wire or dowel in a Tetraxis Star, you see that the shape of the space it passes through is an equilateral triangle.
Picture

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.  As highlighted in yellow, the cross-section of this stick needs to be a 108°- 36°- 36° triangle:
Picture
Picture
Picture
Picture
Picture
Picture

Different kinds of woods can be mixed and matched to create lots of coloring patterns.

Picture
pau amarillo, holly, chakte viga
Picture
wenge, bubinga, zebrawood, maple, verawood
Picture
photo: John Rausch
Picture
a silicon bronze 6-axis star can fit inside
Picture
jatoba, verawood, maple
Picture
photos: Giro Studio

Shown below in yellow is a 3-axis assembly in the shape of a rhombic triacontahedron that goes together in much the same way.  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.

Picture
Picture
photos by Giro Studio
Picture
photos by John Rausch
Picture

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.

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 kite-shaped cross-section of this stick are both 60 degrees.
Picture
photo by Giro Studio
Picture
photo by John Rausch
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.  The 10-axis sticks are scaled to fit perfectly around the 4” Six-axis sculpture, which surrounds the bronze star.
Picture
Picture
Picture
Picture
Picture
Picture
Here are 90 of the 6-axis sticks connected inside out to completely surround the 10-axis sculpture:
Picture
photo: Giro Studio

Arrays of Sticks and Blocks

Picture
Picture
Picture
Picture
4P1S
Picture
Double Duals, truncated version
The illustration below shows the repeating pattern of rods in a Tetraxis Star when the number of wires in a beam is increased.
Picture
Layer 2 of a Tetraxis Array
Picture
Chamfered Cube
Picture
Chamfered Cube
Kostick Stars
Chewbacca with some of the stars on which the Tetraxis Array assemblies are based.
photo: Boston Globe, 1968
When the round rods are replaced by triangular cross-section sticks, the remaining spaces are shaped like the blocks (rhombic dodecahedrons).  Either the sticks or the blocks alone can fill space, meaning an infinite number of each shape can be tightly packed without leaving any gaps between them. Also, together they are space-fillers.
This is very nicely illustrated in a video by Girls' Angle, a math club for girls in Cambridge, Massachusetts.
Countless variations on these designs can be made by moving beyond the single cell that the set of 12 sticks surrounds.  It's just a matter of choosing how long to make the sticks, how to cut the ends, which sticks and blocks to include, and where to place the magnets.

This example uses 24 sticks in two lengths:

4P1S

Picture
Purpleheart
Picture
Picture
Picture
Ipe and Olive Wood
Picture
approx. 3" diameter
Picture
Longleaf Pine and Mahogany
4P1S Tetraxis Array
Additional pictures of more designs can be seen on this page and this page, and many more on our Facebook page and Youtube channel.
*** To see more photos and videos, visit our Facebook page. ***

Home | About Us | Contact Us | Stars | Star History | Star Photos | Woodwork | Furniture and Cabinetry | Trefoil Knot Table | Magnetic Assemblies | IPP32 Entries | 5T3S | Triacontahedron Box | Quadric Designs |  Polar Zonohedra | vZome Models | Sketchfab | Quintetra  | Tetraxis | Tetraxis Toy | Toy Assembly Instructions | Tetraxis Toy Playdough Activity | Tetraxis Geometry | Logo | Kinds of Woods | Cutoffs | Links | Purchasing
Copyright © 2006-2023 KO Sticks LLC. All rights reserved.