Polycube

Polycube

In recreational mathematics, a polycube is a polyform with a cube as the base form. Consequently they are the three-dimensional analogues of the planar polyominos. The Soma cube and the Bedlam cube are examples of packing problems based on polycubes.

Enumerating polycubes

As with polyominos, polycubes can be enumerated in two ways, depending on whether chiral solids are counted once (both reflections counted together) or twice (each reflection counted as distinct). For example, there is a single chiral tetracubes and 6 tetracubes with mirror symmetry, giving a count of 7 or 8 tetracubes respectively. Unlike with polyominos, the usual counting scheme is the latter one, reflecting the fact that in a physical set of polyominos, chiral forms can just be turned over to become their mirror images, something not possible for polycubes. For example, the Soma cube uses both forms of the chiral tetracube.

Kevin Gong has enumerated polycubes up to n=16. See the external links for a table of these results.

ee also

* polyform
* polyhex
* polyomino
* tessellation

External links

* [http://kevingong.com/Polyominoes/Enumeration.html Kevin Gong's enumeration of polycubes]


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • polycube — noun A polyform made by joining one or more cubes face to face in various arrangements …   Wiktionary

  • Tetromino — A tetromino, also spelled tetramino or tetrimino, is a geometric shape composed of four squares, connected orthogonally. This is a particular type of polyomino, like dominoes and pentominoes are. The corresponding polycube, called a tetracube, is …   Wikipedia

  • Soma cube — The Soma cube is a solid dissection puzzle invented by Piet Hein during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube. The pieces can also be used to make a… …   Wikipedia

  • Blockout — Infobox VG| title = Blockout developer = California Dreams publisher = American Technos Inc. (arcade version) designer = Aleksander Ustaszewski, Mirosław Zabłocki engine = released = Arcade version: vgrelease|NA|October 1989 genre = Puzzle modes …   Wikipedia

  • Mel (langage) — Pour les articles homonymes, voir Mel. MEL Apparu en Février 1998 Auteur …   Wikipédia en Français

  • Pentomino — A pentomino is a polyomino composed of five (Greek πέντε / pente ) congruent squares, connected orthogonally.There are twelve different pentominoes, often named after the letters of the Latin alphabet that they resemble. Ordinarily, the… …   Wikipedia

  • Polyomino — The 18 one sided pentominoes, including 6 mirrored pairs …   Wikipedia

  • Polyiamond — A polyiamond (also polyamond or simply iamond) is a polyform whose base form is an equilateral triangle. The word polyiamond is a back formation from diamond, because this word is often used to describe the shape of a pair of equilateral… …   Wikipedia

  • List of combinatorics topics — This is a list of combinatorics topics.A few decades ago it might have been said that combinatorics is little more than a way to classify poorly understood problems, and some standard remedies. Great progress has been made since 1960.This page is …   Wikipedia

  • List of puzzle topics — This is a list of puzzle topics, by Wikipedia page.See also: * List of impossible puzzles * List of puzzle based computer and video games * List of game topics.* Acrostic * Anagram * Back from the klondike * Burr puzzle * Chess problem * Chess… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”