
My puzzles are
based on the geometry of hexagons, a form appearing frequently in
nature as honeycombs,
the markings on a turtle's shell,
and snowflakes.
As in nature, the puzzles contain layers
of complexity within their outwardly simple forms.

figure
1. the puzzles are based on the geometry of hexagons 




Hexagons
may be evenly divided by bisecting the middle and
sectioning off two exterior parts (figure 2).

figure
2. divided hexagons





After
reassembling the hexagons, the sectioned paths make
unique
closed pathways when the 2D plane is rolled into a tube, and then
into a torus.

figure
3. sectioned pathways 




Contiguous
unique areas on the torus surface are defined by these paths (figure
4). 
figure 4





Filling
the contiguous areas with color highlights the continuity of the
defined area (figure 5). 
figure 5





Both the
Trefoil Knot and StepStar are topologically torus
shapes, and
can be assembled inside out (although the handedness of the Trefoil
Knot will reverse). Furthermore, both puzzles are
subject to the sevencolor theorem for torus shapes; click here for more
information about color research by Stan
Tenen. 
figure 6. a
torus
used with permission





Challenge I:
Each piece has a distinctive field within it (see figure 7). How
many possible ways may the puzzle be assembled? 
figure
7. the
puzzle pieces are based on the regular hexagon, reinterpreted as a
sixsided form with 90 degree angles 



Challenge II:
1) After assembly, paint or mark continuous fields, continuing the
color around the 90 degree edge, but stopping at the field edges
(figure 8).
2) Disassemble the puzzle.
3) Reassemble, colormatching continuous fields.
4) How many possible ways are there to reassemble the puzzle with
continuous color fields? With discontinuous color fields? 
figure 8
