Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Soma cube
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
{{refimprove|date = September 2023}} {{short description|Solid-dissection puzzle}} [[File:Colored-Soma-cube-pieces.jpg|thumb|The pieces of a Soma cube]] [[File:Colored-Soma-cube.jpg|thumb|The same puzzle, assembled into a cube]] The '''Soma cube''' is a [[mechanical puzzle#Assembly|solid dissection puzzle]] invented by Danish polymath [[Piet Hein (scientist)|Piet Hein]] in 1933<ref>{{cite web| url = http://www.fam-bundgaard.dk/SOMA/NEWS/N030310.HTM| title = The birth of SOMA| access-date = 2010-12-04| author = Ole Poul Pedersen| editor = Thorleif Bundgaard|date=February 2010}}</ref> during a lecture on [[quantum mechanics]] conducted by [[Werner Heisenberg]].<ref>Cf. [[Martin Gardner]] (1961).''The 2nd Scientific American Book of Mathematical Puzzles & Diversions''. New York: Simon & Schuster. Reprinted in 1987 by University of Chicago Press, {{ISBN|0-226-28253-8}}, p. 65 ([https://bobson.ludost.net/copycrime/mgardner/gardner02.pdf#page=64 online])</ref> Seven different [[Polycube|pieces made out of unit cubes]] must be assembled into a 3×3×3 cube. The pieces can also be used to make a variety of other [[Three-dimensional space|3D]] shapes. The pieces of the Soma cube consist of all possible combinations of at most four unit cubes, joined at their faces, such that at least one inside corner is formed. There are no combinations of one or two cubes that satisfy this condition, but one combination of three cubes and six combinations of four cubes that do. Thus, 3 + (6 × 4) is 27, which is exactly the number of cells in a 3×3×3 cube. Of these seven combinations, two are mirror images of each other (see [[Chirality (mathematics)|Chirality]]). The Soma cube was popularized by [[Martin Gardner]] in the September 1958 [[Mathematical Games column]] in ''[[Scientific American]].'' The book ''[[Winning Ways for your Mathematical Plays]]'' also contains a detailed analysis of the Soma cube problem. There are 240 distinct solutions of the Soma cube puzzle, excluding rotations and reflections: these are easily generated by a simple [[backtracking search]] computer program similar to that used for the [[eight queens puzzle]].<ref>{{Cite web |last=McKeeman |first=W. M. |last2=Fay |first2=M. J. |last3=Pennello |first3=T. J. |date=February 1978 |title=EFFICIENT SOLUTION OF SPACE-FILLING PUZZLES |url=https://apps.dtic.mil/sti/tr/pdf/ADA052951.pdf |access-date=2025-03-20 |website=apps.dtic.mil}}</ref> [[John Horton Conway]] and [[Michael Guy]] first identified all 240 possible solutions by hand in 1961.<ref name=":0" /> ==Pieces== The seven Soma pieces are six [[polycube]]s of order four, and one of order three: {| | [[Image:Soma-ra.svg|60x40px]] | align="center"|Piece 1, {{nowrap|or "V".}} |- | [[Image:Soma-l.svg|60x40px]] | align="center"|Piece 2, {{nowrap|or "L":}} | A row of three blocks with one added below the left side. |- | [[Image:Soma-t.svg|60x40px]] | align="center"|Piece 3, {{nowrap|or "T":}} | A row of three blocks with one added below the center. |- | [[Image:Soma-s.svg|60x40px]] | align="center"|Piece 4, {{nowrap|or "Z":}} | Bent tetromino with block placed on outside of clockwise side. |- | [[Image:Soma-rscrew.svg|60x40px]] | align="center"|Piece 5, {{nowrap|or "A":}} | Unit cube placed on top of clockwise side. [[Chirality (mathematics)|Chiral]] in 3D. {{nowrap|(Left arm)}} |- | [[Image:Soma-lscrew.svg|60x40px]] | align="center"|Piece 6, {{nowrap|or "B":}} | Unit cube placed on top of anticlockwise side. Chiral in 3D. {{nowrap|(Right arm)}} |- | [[Image:Soma-branch.svg|60x40px]] | align="center"|Piece 7, {{nowrap|or "P":}} | Unit cube placed on bend. Not chiral in 3D.<ref>{{cite web|last=Bundgaard|first=Thorleif|title=Why are the pieces labelled as they are|url=http://www.fam-bundgaard.dk/SOMA/NEWS/N111114.HTM|work=SOMA News|access-date=10 August 2012}}</ref> |} [[Image:Soma-cube-disassembled.jpg|thumb|An easier variant of the puzzle, where alternating cubes have different colors]] ==Production== [[Piet Hein (Denmark)|Piet Hein]] authorized a finely crafted [[rosewood]] version of the Soma cube manufactured by Theodor Skjøde Knudsen's company Skjøde Skjern (of Denmark). Beginning in about 1967, it was marketed in the U.S. for several years by the game manufacturer [[Parker Brothers]]. Plastic Soma cube sets were also commercially produced by Parker Brothers in several colors (blue, red, and orange) during the 1970s. The package for the Parker Brothers version claimed there were 1,105,920 possible solutions. This figure includes rotations and reflections of each solution as well as rotations of the individual pieces. The puzzle is currently sold as a logic game by Piet Hein Trading and by ThinkFun (formerly Binary Arts) under the name Block by Block. ==Solutions== [[File:Soma_cube_puzzle_solution.svg|thumb|One of the possible ways of assembling the Soma cube]] Solving the Soma cube has been used as a task to measure individuals' performance and effort in a series of psychology experiments. In these experiments, test subjects are asked to solve a soma cube as many times as possible within a set period of time. For example, In 1969, [[Edward Deci]], a Carnegie Mellon University graduate assistant at the time,<ref>Pink, Daniel H. (2009). "Drive, The Surprising Truth About What Motivates Us". Riverhead Books.</ref> asked his research subjects to solve a soma cube under conditions with varying incentives in his dissertation work on [[intrinsic motivation|intrinsic]] and [[extrinsic motivation|extrinsic]] motivation establishing the [[social psychological]] theory of [[Motivation crowding theory|crowding out]]. In each of the 240 distinct solutions to the cube puzzle, there is only one place that the "T" piece can be placed. Each solved cube can be rotated such that the "T" piece is on the bottom with its long edge along the front and the "tongue" of the "T" in the bottom center cube (this is the normalized position of the large cube). This can be proven as follows: If you consider all the possible ways that the "T" piece can be placed in the large cube (without regard to any of the other pieces), it will be seen that it will always fill either two corners of the large cube or zero corners. There is no way to orient the "T" piece such that it fills only one corner of the large cube. The "L" piece can be oriented such that it fills two corners, or one corner, or zero corners. Each of the other five pieces have no orientation that fills two corners; they can fill either one corner or zero corners. Therefore, if you exclude the "T" piece, the maximum number of corners that can be filled by the remaining six pieces is seven (one corner each for five pieces, plus two corners for the "L" piece). A cube has eight corners. But the "T" piece cannot be oriented to fill just that one remaining corner, and orienting it such that it fills zero corners will obviously not make a cube. Therefore, the "T" must always fill two corners, and there is only one orientation (discounting rotations and reflections) in which it does that. It also follows from this that in all solutions, five of the remaining six pieces will fill their maximum number of corners and one piece will fill one fewer than its maximum (this is called the deficient piece).<ref name=":0">{{citation|url=http://www.fam-bundgaard.dk/SOMA/NEWS/N030518.HTM|title=The complete "SOMAP" is found|journal=SOMA News|first=William|last=Kustes|date=May 18, 2003|access-date=April 25, 2014}}.</ref> ==Figures== [[File:Soma_cube_figures.svg|thumb|upright=1.5|Selected figures in the SOMA manual]] In addition to constructing a cube, the Soma manual provides assorted figures to construct with the seven pieces. The figure on the right shows solutions to some of the figures in the same colour scheme.<ref>{{Cite web|url=http://fam-bundgaard.dk/SOMA/SOMAPRINT.HTM|title=Thorleif's SOMA page}}</ref> ==Similar puzzles== Another puzzle similar to the Soma cube is the 3D [[pentomino]] puzzle, which can fill boxes of 2×3×10, 2×5×6 and 3×4×5 units. The [[Bedlam cube]] is a 4×4×4 sided cube puzzle consisting of twelve [[pentacube]]s and one [[Polycube|tetracube]]. The [[Diabolical cube]] is a puzzle of six polycubes that can be assembled together to form a single 3×3×3 cube. [[Eye Level Learning|Eye Level]] also makes use of the Thinking Cube (once students are in levels 30-32 of Basic Thinking Math or levels 29-32 of Critical Thinking Math), as one of its Teaching Tools, similar to the Soma cube. [[Rubik's Bricks]],<ref>{{Cite web | title=TwistyPuzzles.com > Museum > Rubik's Bricks | url=https://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=4300 | archive-url=https://web.archive.org/web/20130916170700/http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=4300 | access-date=2024-12-24 | archive-date=2013-09-16}}</ref> a puzzle produced under the [[Rubik's Cube|Rubik's]] branding, is a similar puzzle made of 27 cubes, but the pieces are formed by joining cubes either by faces or by edges. There are exactly 9 such ways to join three cubes, so the puzzle can make a 3x3x3 cube. The individual cubes are colored in such a way as to give a unique solution. ==See also== * [[Bedlam cube]] * [[Conway puzzle]] * [[Diabolical cube]] * [[Herzberger Quader]] * [[Pentomino]] * [[Slothouber–Graatsma puzzle]] * [[Snake cube]] * [[Tangram]] * [[Tetromino]] * [[Tromino]] ==References== {{Reflist}} ==External links== {{Commons|Soma cube|Soma cube}} * {{Cite web| title=SOMA-CUBE | url=http://www.mathematik.uni-bielefeld.de/~sillke/POLYCUBE/SOMA/cube-secrets | archive-url=https://web.archive.org/web/20010731021245/http://www.mathematik.uni-bielefeld.de:80/~sillke/POLYCUBE/SOMA/cube-secrets | archive-date=2001-07-31}} * [http://mathworld.wolfram.com/SomaCube.html Soma Cube – from MathWorld] * [http://www.fam-bundgaard.dk/SOMA/SOMA.HTM Thorleif's SOMA page] * [https://www.youtube.com/watch?v=9ngzN2RQEtM SOMA CUBE ANIMATION by TwoDoorsOpen and Friends] {{Polyforms}} {{Authority control}} [[Category:Mechanical puzzle cubes]] [[Category:Tiling puzzles]]
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)
Pages transcluded onto the current version of this page
(
help
)
:
Template:Authority control
(
edit
)
Template:Citation
(
edit
)
Template:Cite web
(
edit
)
Template:Commons
(
edit
)
Template:ISBN
(
edit
)
Template:Nowrap
(
edit
)
Template:Polyforms
(
edit
)
Template:Refimprove
(
edit
)
Template:Reflist
(
edit
)
Template:Short description
(
edit
)
Template:Sister project
(
edit
)