TOPICS
Search

Polycube


Polycube11
Polycube21
Polycube31
Polycube32
Polycube41
Polycube42
Polycube43
Polycube44
Polycube45
Polycube46
Polycube47
Polycube48

Three-dimensional generalization of the polyominoes to n dimensions. The number of polycubes N(n) composed of n cubes are 1, 1, 2, 8, 29, 166, 1023, ... (OEIS A000162; Ball and Coxeter 1987).

Polycubes may be conveniently represented and visualized in the Wolfram Language using ArrayMesh.

There are 1390 distinct ways to pack the eight polycubes of order n=4 into a 2×4×4 box (Beeler 1972).


See also

Conway Puzzle, Cube Dissection, Diabolical Cube, Pentacube, Polyform, Slothouber-Graatsma Puzzle, Soma Cube

Explore with Wolfram|Alpha

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 112-113, 1987.Beeler, M. Item 112 in Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, pp. 48-50, Feb. 1972. http://www.inwap.com/pdp10/hbaker/hakmem/polyominos.html#item112.Bouwkamp, C. J. "Packing Handed Pentacubes." In The Mathematical Gardner (Ed. D. Klarner). Boston, MA: Prindle, Weber, 1981.Clarke, A. L. "Polycubes." http://www.recmath.com/PolyPages/PolyPages/Polycubes.html.Gardner, M. The Second Scientific American Book of Mathematical Puzzles & Diversions: A New Selection. New York: Simon and Schuster, pp. 76-77, 1961.Gardner, M. "Polycubes." Ch. 3 in Knotted Doughnuts and Other Mathematical Entertainments. New York: W. H. Freeman, pp. 28-43, 1986.Keller, M. "Counting Polyforms." http://members.aol.com/wgreview/polyenum.html.Sloane, N. J. A. Sequence A000162/M1845 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Polycube

Cite this as:

Weisstein, Eric W. "Polycube." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Polycube.html

Subject classifications

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy