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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.
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1. the puzzles are based on the geometry of hexagons |
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Hexagons
may be evenly divided by bisecting the middle and
sectioning off two exterior parts (figure 2).
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2. divided hexagons
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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.
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3. sectioned pathways |
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Contiguous
unique areas on the torus surface are defined by these paths (figure
4). |
figure 4
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Filling
the contiguous areas with color highlights the continuity of the
defined area (figure 5). |
figure 5
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Both the
Trefoil Knot and Step-Star 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 seven-color theorem for torus shapes; click here for more
information about color research by Stan
Tenen. |
figure 6. a
torus
used with permission
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Challenge I:
Each piece has a distinctive field within it (see figure 7). How
many possible ways may the puzzle be assembled? |
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7. the
puzzle pieces are based on the regular hexagon, re-interpreted as a
six-sided form with 90 degree angles |
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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) Re-assemble, color-matching continuous fields.
4) How many possible ways are there to re-assemble the puzzle with
continuous color fields? With dis-continuous color fields? |
figure 8
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