# Diabolical cube

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{{Short description|Three-dimensional packing puzzle}}
thumb|left|A disassembled diabolical cube and many assembled ones.
thumb|A solution for the Diabolical Cube puzzle – swapping the 2-cube (red) and 4-cube (yellow) blocks gives another
The '''diabolical cube''' is a three-dimensional [dissection puzzle](/source/dissection_puzzle) consisting of six [polycube](/source/polycube)s (shapes formed by gluing [cube](/source/cube)s together face to face) that can be assembled together to form a single 3&nbsp;×&nbsp;3&nbsp;×&nbsp;3 cube.<ref>{{mathworld | title = Diabolical Cube | urlname = DiabolicalCube }}</ref><ref name="coffin">{{citation
 | last = Coffin
 | first = Stewart T.
 | contribution = Cubic Block Puzzles: The 3 x 3 x 3 Cube
 | publisher = Oxford University Press
 | title = The Puzzling World of Polyhedral Dissections
 | url = http://www.johnrausch.com/PuzzlingWorld/chap03a.htm
 | year = 1991
 | access-date = 2006-08-25
 | archive-url = https://web.archive.org/web/20061031104100/http://www.johnrausch.com/PuzzlingWorld/chap03a.htm
 | archive-date = 2006-10-31
 | url-status = dead
 }}.</ref>
The six pieces are: one dicube, one tricube, one tetracube, one pentacube, one hexacube and one heptacube, that is, polycubes of 2, 3, 4, 5, 6 and 7 cubes.

There are many similar variations of this type of puzzle, including the [Soma cube](/source/Soma_cube) and the [Slothouber–Graatsma puzzle](/source/Slothouber%E2%80%93Graatsma_puzzle), two other  [dissections](/source/Dissection_(geometry)) of a 3&nbsp;×&nbsp;3&nbsp;×&nbsp;3 cube into polycubes which use seven and nine pieces respectively. However, {{harvtxt|Coffin|1991}} writes that the diabolical cube appears to be the oldest puzzle of this type, first appearing in an 1893 book ''Puzzles Old and New'' by [Professor Hoffmann](/source/Professor_Hoffmann) (Angelo Lewis).<ref name="coffin"/>

Because all of the pieces have only a single layer of cubes, their shape is unchanged by a mirror reflection, so a mirror reflection of a solution produces either the same solution or another valid solution. The puzzle has 13 different solutions, if mirrored pairs of solutions are not counted as being distinct from each other.<ref name="coffin"/>{{Clear|left}}

== References ==
{{reflist}}

Category:Tiling puzzles
Category:Mechanical puzzle cubes

{{puzzle-game-stub}}

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Adapted from the Wikipedia article [Diabolical cube](https://en.wikipedia.org/wiki/Diabolical_cube) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Diabolical_cube?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.