10182
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Delannoy Number Carpet
Michael Schreiber
A 2-pire Map
Ed Pegg Jr
Escher's Method Applied to Created Celtic Designs
Karl Scherer
Nowhere-Neat Tilings of the Plane, Part 2
Karl Scherer
Nowhere-Neat Tilings of the Plane
Karl Scherer
Four-Color Maps
Ed Pegg Jr
Replicating Patterns in 2D Binary Cellular Automata with the Parity Rule
Hiroki Sayama
Stable Marriages
Seth J. Chandler
Knight Paths
Taylor McCreary
Relations and Graphs
Jaime Rangel-Mondragon
Related Topics
Discrete Mathematics
Graph Theory
Patterns
Tiling
High School Finite Mathematics
High School Mathematics
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+