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Polycube Snakes
The
,
and
cubes can be filled with a polycube "snake" that turns by right angles at every step. The solutions for these three cubes are given here.
The display of the polycubes is optional; their positions are represented by black points connected by a polyline.
Such a snaking path can be found for all cuboids
except for the following cases:
and
,
odd,
odd,
.
(Karl Scherer 1982; the proof is very easy.)
Contributed by:
Karl Scherer
THINGS TO TRY
Rotate and Zoom in 3D
SNAPSHOTS
RELATED LINKS
Hilbert Curve
(
Wolfram
MathWorld
)
Plane-Filling Function
(
Wolfram
MathWorld
)
PERMANENT CITATION
Karl Scherer
"
Polycube Snakes
"
http://demonstrations.wolfram.com/PolycubeSnakes/
Wolfram Demonstrations Project
Published: March 7, 2011
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