Magic Polyhedra* Patents - Brandeisstorer/JimPuzzles/... · Or search on eBay for related puzzles...

01/08/2007 03:34 PMThe Magic Polyhedra Patent Page

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Magic Polyhedra* PatentsBy Joshua Bell. Last updated May 07, 2006.

Background | Resources | Solution | Mechanics | Patents | Collection

BackgroundIn the early 1980's a fad briefly swept most of the civilized world - the Rubik's Cube®. This unassuming toy inspiredbooks, competitions, songs, and even a cartoon series on television, along with several similar polyhedral puzzles. Ibriefly toyed with the puzzle but I was more fascinated with the mechanical aspects than the mathematical puzzle. Thelatter was answered handily with books (which I had) or persistence (which I did not), but the former was moremysterious. Fortunately it's easy to crack open a cube given a butter knife, with little harm done.

In late 2000 I ran across a discussion of different magic polyhedra beyond the 3x3x3 cube - within the larger family ofsequential movement puzzles - and was briefly hooked. With a few hundred dollars spent via mail orders and on eBay Isecured myself a nice collection. I even dabbled with making some custom puzzles. I'm still lousy at solving the darnedthings, but I appreciate them even more than I did in 1980.

ResourcesThere are hundreds of cube-related pages out there. These are some of my favorites.

Hendrik Haak's Puzzle Shop & Museum - many rare puzzles on display, and several for saleTwistyPuzzles.com - an extremely extensive collection of pictures of twisty puzzlesJaap's Puzzle Page is one of the best collections of solutions and musings on the possibilities and mechanics ofpuzzles. Especially distinctive is his page of Ideas for other puzzles.Puzzler - a shareware Windows app that lets you play with nearly every twisty puzzle ever devised, includingones never constructed in the real world.Twisty Megasite - a puzzle collection and discussion forum.Cube-Lovers - an MIT-based mailing list running from 1980 through 2000. The archive is available atftp://ftp.ai.mit.edu/pub/cube-lovers or via various web archives, such as http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/Magic Cube 4D - why stop at three dimensions?

Manufacturers and Suppliers:

Rubiks.com - home page for the Rubik's Cube.Meffert's Puzzles - home page for Uwe Meffert's range of puzzles, including the Skewb family, Pyraminx,Pyramorphix, and Megaminx.Hockey Puck Puzzle

Or search on eBay for related puzzles up for auction. But please check out the above suppliers first - you can order



brand new 4x4x4 directly from Rubiks.com for about US$20 or a 5x5x5 directly from Meffert's for about US$30, sothere's no need to pay high prices in an auction.

And some minor sites, worth visiting:

Puzzle Museum - Sequential Puzzles - has photos of some rare puzzlesA Japanese collector's extensive collection of twisty and other puzzles and toysGeorges Helm's puzzle collection

SolutionThere is really only one solution that you need for the majority of Rubik-like puzzles, especially if - like me - you'relousy at memorizing things and don't plan to solve the puzzle daily for fun and profit. Visit Alan Hensel's page, "How toSolve Almost Any Rubik-Like Puzzle" for a very detailed walk through the solution. Here's the short version:

What you need:

A sequential movement puzzleA piece of paper and pencilThe ability to solve one layer (or face or slice or equivalent) of the puzzle.The ability to describe abstract operations necessary to solve the puzzle; e.g., "I need to cycle these three edgesand rotate these two corners."A notation for moves on the puzzle (e.g. FBLRUD, F'B'L'R'U'D', where x' is the inverse of x)The magic formula: P XsX's' P'

Steps (places where you actually move the puzzle are underlined):

. 1 Get the puzzle as close to a solved state as you can by whatever means you like.

. 2 Invent, write down, and perform any sequence of moves, P, which brings all of the pieces you want to solveonto a single layer (L).

. 3 Conceptually group the remaining moves and flips into a pair of two symmetric abstract operations (M and M').

. 4 Invent, write down, and perform any sequence of moves, X, which performs M but leaves layer L untouched atthe end of the sequence; the rest of the puzzle can be messed up.

. 5 Perform the single move s which is a rotation of L which gets pieces corrected by M out of the way and gets thepieces to be corrected by M' into their place.

. 6 Perform the sequence X' - that is, do the inverse of each of the steps you wrote down in reverse order.

. 7 Perform the single move s' which puts layer L back where we had it in step 3 - except for M and M'.

. 8 Perform the sequence P' which puts everything back where you started.

And some comments:

You can do this piecemeal - if you have corners and edges that need work, you can simplify things by dealingwith corners first then edges, or vice versa - the puzzle doesn't care how many steps you break it down into.When inventing P and X you may find it convenient to write the steps down as you go.To get through Step 3 you may need to break down a seemingly simple operation into two parts; e.g. if threeedges (ABC) need to be cycled, consider it instead as two swaps (AB, BC). In this case, during Step 5 somepieces touched by M will be set up to be touched a second time by M'.This scheme won't work for some puzzles; when in doubt I always start with Jaap's Puzzle Page.

Mechanics

Common features

Many puzzles are built around either a central "spider" mechanism (shafts joining at the center of the puzzle), acentral sphere, or some intermediate combination. A spider is used in the 3x3x3 cube, the Skewb, and theImpossiball. The Pyraminx and 4x4x4 cube are based around a central sphere.



In 2x2x2 puzzles, one octant must remain fixed to the central mechanism. If all eight were identical the internalmechanism could drift out of alignment with the rest of the puzzle, rendering it impossible to twist on two of thethree axes.NxNxN puzzles where N is even are often based on a N+1 spider with the axis concealed or shared by thecenter pieces.A variant of the spider mechanism is the stellated polyhedron, where a core polyhedron is extended withpyramidal tips which rotate. The "cubie" analogs sit between these tips are attached to the mechanism by gapsin the base of the tips. When the tips rotate, the "cubies" are interchanged. This is used in the Alexander's Star(where the internal mechanism is a small stellated dodecahedron) and Dino Cube (where the internalmechanism is a stellated octahedron, or stella octangula).Magnets are rarely used in mass-produced puzzles, although often suggested as possible mechanisms.

Notation & Terminology

NxNxN - a puzzle in the family of Rubik's Pocket Cube (2x2x2), Rubik's Cube (3x3x3), Rubik's Revenge (4x4x4)and the Professor Cube (5x5x5). Each face or slice may be rotated 90°, 180° or 270°. Pieces of the same type(e.g. edges, corners, centers) can be swapped.XxYxZ - like an NxNxN a puzzle, but with different numbers of cubies on different axes. Includes the MagicDomino, with a 3x3x2 mechanism. Typically, sides which do not match other sides must be rotated 180° ratherthan 90° to permit the puzzle to continue to be manipulated.A trivial extension is one that does not affect the solvability of a puzzle, beyond rotations of the single extensionpiece which do not affect any other part of the puzzle. An example are the tips of a Pyraminx (which merelyrotate around their single point of attachment to an otherwise external the puzzle), and the purely decorative,non-rotating tips of the extended 3x3x3 cubes (e.g. 3x3x"5" - wherein the top and bottom layer of cubies aredecorated with another layer of fixed cubies).A non-trivial extension is a modification of an existing or more fundamental puzzle type with additional piecesthat may be interchanged. Typically, these may only be interchanged with each other. The canonical example isthe Abu-Shumays work on extending the 2x2x2 mechanism with an additional layer of 4 cubies. Theseextension cubies are not uniquely fixed to cubies within the base puzzle and may be rotated as a group. Addingextension cubies to more faces allows the extensions to be interchanged among the faces when the base 2x2x2mechanism is twisted along a given axis, producing a new, non-decorative aspect to the puzzle. Higher ordercubes (4x4x4 and 5x5x5) can be thought of as extreme non-trivial extensions of the 2x2x2 and 3x3x3mechanism.(N+a)x(N+b)x(N+c) - a new notation (unique to this page) to describe an NxNxN puzzle with non-trivialextensions.Octahedrons with triangular cubies may be face-centered (a face rotates) or vertex-centered (a pyramid arounda corner rotates). The order of an octahedral puzzle refers to the number of unit-triangles along one edge,regardless of triviality.A puzzle is said to be deep cut if there is a cut which bisects the entire puzzle. Thus, the 2x2x2 cube andSkewb are deep cut while the 3x3x3 cube is not.

PatentsThanks to the US Patent and Trademark Office and the European Patent Office it is possible to use the web to viewpatents for almost anything that has been patented within the last thirty-odd years. This is an attempt at a somewhatcomprehensive list of interesting patents relating to magic polyhedra.

Details Description Representative ImagePatentNumber:

US3637215PopularName:

Spinout

Inventor(s): William KeisterDate Filed: December 22,

1970Date Issued: January 25, 1972



PatentNumber:

US3655201PopularName:Inventor(s): Larry D. NicholsDate Issued: April 11, 1972

PATTERNFORMINGPUZZLE ANDMETHOD WITHPIECESROTATABLE INGROUPS

PatentNumber:


Entrapment

Inventor(s): Jeffrey D.Breslow

Date Filed: November 3,1980

Date Issued: November 8,1983

PatentNumber:


Billion Barrel andTrillion

Inventor(s): Gunpei Yokoi(Nintendo)

Date Filed: December 30,1980

Date Issued: March 15, 1983

PatentNumber:


Missing Link

Inventor(s): Steven P.Hanson; JeffreyD. Breslow

Date Filed: January 12, 1981Date Issued: February 15,

1983

PatentNumber:

BE887875PopularName:

Rubik's Cube

Inventor(s): Ernö RubikDate Filed: March 10, 1981Date Issued: July 1, 1981

The original patentfor the 3x3x3Rubik's Cube andone mechanismfor the 2x2x2Pocket Cube.



PatentNumber:

EP0042695PopularName:

Pyraminx

Inventor(s): Uwe MeffertDate Filed: June 10, 1981

The originalPyraminx - anorder-3tetrahedron withrotating verticiesand trivial tips.The core is acentraltetrahedron,sphere or four-armed spider.Attached to thisare fouroctahedrons. Eachoctahedron has atrivial rotating tipand between theoctahedrons arethe six mobiletetrahedral edgepieces. The patentalso describes thestellated pyraminx.

PatentNumber:


Rubik's Snake

Inventor(s): Kenji KomiyaDate Filed: July 20, 1981Date Issued: March 29, 1983

PatentNumber:


Rubik's Snake

Inventor(s): Erno Rubik(Politoys)

Date Filed: July 24, 1981

PatentNumber:


Rubik's Fifteen

Inventor(s): Erno RubikDate Filed: September 1,

1981

PatentNumber:


Puzzler

Inventor(s): Douglas A. Engel(GeneralSymmetrics, Inc.)

Date Filed: September 21,1981




PatentNumber:


Rubik's Cheese

Inventor(s): Erno Rubik(Konsumex)


A single layerpuzzle with sixpieces.

PatentNumber:

DE3204033PopularName:

Thomas Ball

Inventor(s): Dr. GilbertObermair

Date Filed: February 5, 1982Date Issued: August 25, 1983

Anothermechanismequivalent to theImpossiball.Twenty triangularcaps twist ingroups of fivearound a commonvertex. Thepopular puzzle hasa cap on eachvertex to make thepuzzle decoratedand shaped like asoccer ball, but thepatent proposesother outer shapessuch as adodecahedron oricosahedron.

PatentNumber:


Crossover

Inventor(s): Gunpei Yokoi(Nintendo)

Date Filed: February 12,1982

Date Issued: September 6,1983

PatentNumber:


Orb-it

Inventor(s): Christopher C.Wiggs &Christopher J.Taylor


PatentNumber:

GB2084471PopularName:

Rubik'sOctahedron

Inventor(s): Ernö RubikDateIssued:

April 15, 1982

An order-2 face-centeredoctahedron basedon a Pyraminx-likecentral sphere.The face-centersare affixed to thesphere and thevertices floataround.



PatentNumber:


Equator

Inventor(s): Wilton R. GreeneDate Filed: July 30, 1982Date Issued: June 5, 1984

PatentNumber:

US4344623PopularName:Inventor(s): Toshiyuki IsobeDate Issued: August 17, 1982

A 2x2x2mechanism(depicted is avertical slicethrough a diagonalplane).

PatentNumber:


Hungarian Globe

Inventor(s): Molnar FerencDate Issued: October 14, 1982

PatentNumber:


Megaminx(Bandelow)

Inventor(s): Dr. ChristophBandelow;Helmut Corbeck

Date Issued: October 14, 1982

PatentNumber:

WO8203564PopularName:

HungarianSupernova

Inventor(s): Szlivka FerencDateIssued:

October 28, 1982



PatentNumber:


Babylon Tower

Inventor(s): ARXON SPIEL &FREIZEIT GMBH(DE)

Date Issued: December 2,1982

PatentNumber:

GB2100134PopularName:

Inversion Cube

DateIssued:

December 22,1982

PatentNumber:


Puzzle Toy (likeequator withdouble rows, noorientations)

Inventor(s): Evangelos T.Kikis

Date Filed: February 3, 1983

PatentNumber:


Magic Domino

Inventor(s): Ernö RubikDate Issued: March 29, 1983

The 3x3x2 Rubik'sDomino. Twomechanisms aresuggested - onewith a six armedspider (four ofwhich are sliced inhalf vertically andterminate withinthe body), andone that dispenseswith the spider infavor of a tab-and-groovemechanism.

PatentNumber:


Rubik's PocketCube

Inventor(s): Ernö RubikDate Issued: March 29, 1983

A 2x2x2mechanism. Sevenpieces are held inplace against aneighth by threearms.



PatentNumber:


Pyramorphix

Inventor(s): Manfred FritscheDate Issued: August 11, 1983

PatentNumber:


MagicOctahedron

Inventor(s): Karl RohrbachDate Issued: September 1,

1983

PatentNumber:

US4405131PopularName:Inventor(s): Tibor HorvathDate Issued: September 20,

1983

An elaborate2x2x2 mechanismutilizing nestedshells. The cubiesproject arms into acentral sphere withtracks to guidetheir movement.

PatentNumber:


Rubik's Calendar

Inventor(s): Marvin A.Silbermintz


A calendar cube.The patentincludes thesticker layout anda solution.

PatentNumber:


Rubik's Revenge

Inventor(s): Peter SebestenyDate Issued: December 20,

1983

A 4x4x4 cube;pieces orbit acentral sphere withprojecting capsthat both holds theface-centers andprovides a trackfor their rotation.



PatentNumber:

US4437667PopularName:Inventor(s): Ronald L. MillerDate Issued: March 20, 1984

Just a 3x3x3cube, but thepatent is for avariety ofScrabble-likegames playable onthe surface by theuse of detachablestickers or markersfor the cubiefaces.

PatentNumber:

US4441715PopularName:Inventor(s): Stephen C. TitusDate Issued: April 10, 1984

A sphere with 6interchangeablesegments. Like aMasterball withoutthe latitudinalslices.

PatentNumber:

JP60222076PopularName:

Master RainbowCube

Inventor(s): WatanabeYasunari, IkegamiYuuji

Date Filed: April 18, 1984

This puzzle is tothe Rainbow Cubeas the 5x5x5 is tothe 3x3x3.Amazing!

PatentNumber:

US4451039PopularName:Inventor(s): Clarence W.

Hewlett, Jr.Date Issued: May 29, 1984

An order-3 face-centered magicoctahedron. Thetips are non-trivialand none of theexterior pieces arefixed in place. Thecentral mechanismis a stellaoctangula withrotating tips,surrounded by sixcorner octahedra,twelve edgeoctahedra, andtwenty four facetetrahedra.

PatentNumber:


Halpern-MeierPyramid

Inventor(s): Benjamin R.Halpern

Date Issued: June 12, 1984

The Halpern-MeierPyramid. Theedges and tipsproject feet intothe center of thetetrahedron whichcombine to form asphere. The face-centers connect inthe center of thesphere and holdeverythingtogether. Alsoincludes aMegaminx variantand a truncatedtetrahedron withface centers,corners andedges, and asuggestion for



what will later beknown as"bandaging".

PatentNumber:

US4473228PopularName:Inventor(s): John R. HartDate Issued: September 25,

1984

A possiblemechanism for anImpossiball - anicosahedron onwhich each "cap"of 5 faces may berotated, allow thefaces to migratearound thesurface.

PatentNumber:


Impossiball

Inventor(s): William O.Gustafson


The canonicalImpossiballmechanism - anicosahedron onwhich each "cap"of 5 faces may berotated, allow thefaces to migratearound thesurface. With onepiece removed thetoy still holdstogether and thegame turns into avariant of the 15-Puzzle; adjacenttriangular piecesmay be slid intothe gap.

PatentNumber:

US4474377PopularName:Inventor(s): Jonathan J.

AshleyDate Issued: October 2, 1984

A combination of a2x2x2 cube and aDino cube. Theinternalmechanism is astella octangulafrom a Dino Cubewith rotating tips(like anAlexander's Star),but deep-cut withan embedded2x2x2 mechanism.

PatentNumber:


Star of David

Inventor(s): Israel GoldfarbDate Issued: January 9, 1985

The puzzle hasthe shape of astella octangula.The coreoctahedron has a2x2x2 mechanismlike a modifiedPyramorphix, butthe tips can rotateas well.

PatentNumber:

US4500090PopularName:Inventor(s): Antoliono NietoDate Issued: February 19,

1985

Very similar to theAlexander's Star,but with a morecomplicatedmechanism ofgrooves.



PatentNumber:


Alexander's Star

Inventor(s): Adam AlexanderDate Issued: March 26, 1985

The popularAlexander's Starpuzzle; a greatdodecahedronwhere each vertexrotates. Thecentral mechanismis a small stellateddodecahedron witha dodecahedralcore; each tiprotates.

PatentNumber:


Skewb Diamond

Inventor(s): Michael RichterDate Issued: April 18, 1985

PatentNumber:

US4513970PopularName:Inventor(s): Ovidiu Opresco;

Jon D. MarinescoDate Issued: April 30, 1985

A 2x2x2mechanism using8 magnets oneach plane (6 perpiece). Non-cubical shapes aresuggested, suchas off -center ortiled cuts in cubes,off -center cuts incubes, and visuallyattractive egg-shaped puzzles.

PatentNumber:

US4522401PopularName:Inventor(s): William O.

GustafsonDate Issued: June 11, 1985

A spherical 3x3x3with no internalspider mechanism;the shell is heldtogether in amanner similar tothe design ofUS4441715.

PatentNumber:

US4540177PopularName:Inventor(s): Tibor HorvathDate Issued: September 15,

1985

A 4x4x4mechanism basedaround anembedded 2x2x2mechanism. Theface centers havefeet embedded ina central sphere.The edge pieceslock underadjacent centers,and corner pieceslock underadjacent edgesand centers justlike on the 3x3x3cube.



PatentNumber:

US4557484PopularName:Inventor(s): Benjamin F.

Sherman, Jr.;Samuel Francis

Date Issued: December 10,1985

An elegantspherical 2x2x2mechanism withthe mobile octantsriding around ahollow centralsphere on tracks.Further, there isthe suggestion thatat eachintersection of fourpieces the tipsmay be swappedby rotation, thusyielding a(2+2)x(2+2)x(2+2)mechanism.

PatentNumber:

US4558866PopularName:Inventor(s): William L. AlfordDate Issued: December 17,

1985

A variety ofdesigns: aPyraminx withouttrivial tips and aTetraminx; a face-centered order-2octahedron; aPentUltimatemechanism withmagnetic piecesaround a metalsphere

PatentNumber:


Manipulativeamusementdevice(hexagonal ring)

Inventor(s): David B. AyersDate Filed: January 6, 1986

PatentNumber:

US4586713PopularName:Inventor(s): Ibrahim K. Abu-

Shumays; MaryD. Abu-Shumays

Date Issued: May 6, 1986

A generalizedfamily of star -prisms puzzles; allare three layerstall.

PatentNumber:

SU1232171PopularName:

Russian MasterPyraminx

Inventor(s): Alexsandr A.Ordynets




PatentNumber:




First, yet another2x2x2 mechanism,followed by anapplication of it tovarious regularand irregularpolyhedra. Next, ageneralizedextensionmechanism formaking a2x2x(2+1) - andthe application ofthat to polyhedra.Then duplicatingthe extension toproduce a2x2x(2+2), and thelogical follow-on of2x(2+2)x(2+2) and(2+2)x(2+2)x(2+2)puzzles, andsuggestions forpolyhedra toembed themechanism within.It goes on tosuggest a possibletrue 4x4x4mechanism, butdoes not givedetails. Wow!

PatentNumber:

US4593908PopularName:Inventor(s): Baky B. IbrahimDate Issued: June 10, 1986

A deep-cut order-2 vertex-centeredoctahedron basedon a 2x2x2embedded withinan cuboctahedronwith pyramidal tipsthat rotate on theunderlying facesand split alongtheir edges.

PatentNumber:


Professor's Cube

Inventor(s): Udo KrellDate Issued: July 15, 1986

Another heftypatent. This onestarts with adeeply truncatedcube and works itsway up to theamazing 5x5x5mechanism. It alsosuggests a deep-cut dodecahedronpuzzle (whichresembles but isdistinct from thePyraminx Crystal)

PatentNumber:


Rubik's Magic

Inventor(s): Erno RubikDate Filed: July 28, 1986Date Issued: August 11, 1987



PatentNumber:


Rubik's electroniccube

Inventor(s): Gabor Biro;Robert Breitner;Gabor Fazekas;Istvan Hejjas;Peter Niklai; ErnoRubik; KarolySzabo; IstvanTothmatyas


Date Issued: April 4, 1989

PatentNumber:




The name of thepatent is "Starprism puzzlesgeneralized" and itreally is just ageneralization ofthe earlier patentUS4586713 by thesame inventors.

PatentNumber:




The outer puzzleis a rhombicdodecahedronwhere each vertexrotates. Internally,the mechanism issimilar to theAlexander's Star -an internalcuboctahedronwith rotating tipsadded to both thesquare andtriangular faces,which trap thesurface pieces incentral notches.

PatentNumber:


Gripple

Inventor(s): Murray J. GouldDate Filed: June 25, 1987Date Issued: April 5, 1988

PatentNumber:

DE8707783UPopularName:

Pyraminx Crystal

DateIssued:

July 16, 1987



PatentNumber:


Padlock

Inventor(s): Ira FriedmanDate Filed: October 5, 1987Date Issued: November 8,

1988

PatentNumber:


Atomic Chaos

Inventor(s): ChristophHausammann(Joker SA/AG


PatentNumber:




Two octahedralvariations on the3x3x3 mechanism;one resembles theTrajber'sOctahedron(essentially anextremelytruncated cube),the other the StarPuzzler but withfixed rather thantrivial tips. Thenan icosahedralpuzzle where thevertex-caps arefixed but overlapto create mobileedge pieces.

PatentNumber:


Topspin

Inventor(s): FerdinandLammertink(Binary Arts)

Date Filed: September 2,1988

PatentNumber:


Cross

Inventor(s): MargaritisAthanasios

Date Filed: October 20, 1988



PatentNumber:


Manipulativeamusementdevice(hexagonal ring)

Inventor(s): David B. AyersDate Filed: January 11, 1989

PatentNumber:

US4836549PopularName:Inventor(s): James T. FlakeDate Issued: June 6, 1989

A stella octangulain the form of twointersecting order-four tetrahedrons.The tips are trivial(like thePyraminx). Sub-pyramids of size 2(just like on thePyraminx) may berotated 120°,cycling threepieces. Movingone layer deeper,another rotation of120° may beperformed whichmoves the sub-pyramid plus the"base" of the othertetrahedron.

PatentNumber:


Rubik's Clock

Inventor(s): ChristopherCharles Wiggs


PatentNumber:


Masterball

Inventor(s): Geza GyovaiDate Issued: August 15, 1989

The Masterballmechanism.Essentially Titus'six segmentsphere (which thispatent cites asprior art) with theaddition of fourbands (two polar,two equatorial)that rotate aroundthe surfaceorthogonally to theunderlyingsegments.

PatentNumber:

US4865323PopularName:Inventor(s): Paul A.

HeusinkveldDate Issued: September 12,

1989

Like a super-Masterball with sixlatitudinalsegments vs. fouron the Masterball.The mechanismfor the surfacebands is muchmore robust inappearance,however.



PatentNumber:

US4872682PopularName:Inventor(s): Ravi

Kuchimanchi;Madhukar N.Thakur


A 3x3x3 combinedwith a "9-puzzle";the faces on thecube can be slidaround exactly asin a 15-puzzle;manipulating the3x3x3 mechanismmigrates the emptysquare betweenfaces.

PatentNumber:


Luminations

Inventor(s): Donald C. Miffitt;Angelo Tortola;Charles S. Sebor;Robert L.Halliday



PatentNumber:

US4889340PopularName:Inventor(s): Wilton R. GreeneDate Issued: December 26,

1989

A variant of theEquator puzzle,where threeintersecting bandson the surface ofa cube allowsquare pieces toslide around andmove betweenbands.

PatentNumber:


Tricky Disky

DateIssued:

December 28,1989

PatentNumber:


Roundy (4 faces)

Inventor(s): Fritz GruberDate Filed: April 28, 1990



PatentNumber:


Rubik's Dice

Inventor(s): Jozsef Bognar;Erno Rubik


Date Issued: February 9, 1993

PatentNumber:


Puck

Inventor(s): Zoltan Pataki;Geza Csomos

DateIssued:

March 7, 1991

PatentNumber:


Equator

Inventor(s): Daniel E. GreenDate Filed: May 14, 1991

PatentNumber:


Puzzle Device(like Mozaika butdifferentmechanism)

Inventor(s): Ming-Zen LiuDate Filed: July 9, 1991

PatentNumber:


Puzzle Can

Inventor(s): Karl Blankenburg,Karl V.Blankenburg,Duane Rode

Date Filed: August 5, 1991Date Issued: May 26, 1992



PatentNumber:


Back Spin


Date Filed: January 15, 1992

PatentNumber:


Wisdom Ball

Inventor(s): Yan-Ju HsunDate Filed: May 18, 1992

PatentNumber:


Smart Alex

Inventor(s): Dumitru A. PopDate Issued: May 26, 1992

A cube withhexagonsprojecting fromfour sides. Thehexagons aredivided into sixtriangularsegments androtate around theircenters. The entirecube is split at theequator androtates,interchangingpieces of adjacenthexagons. A verysimple mechanismbut a nice puzzle.

PatentNumber:


Assembly Cube

Date Filed: August 28, 1992DateIssued:

December 21,1993

PatentNumber:


Assembly cube

Inventor(s): Hank Chang(FamwealthInternational Inc.,TW)

Date Filed: August 28, 1992Date Issued: December 21,

1993



PatentNumber:


Pyrix

Inventor(s): Jaap Koops; JanEssebaggers


PatentNumber:

RO106960PopularName:Inventor(s): Florian RadutDate Filed: October 27,

1992

A 4x4x4mechanism with aspherical core.

PatentNumber:

RO106962PopularName:Inventor(s): Florian RadutDate Filed: December 14,

1992

The classic 3Dmarble variation offamous the 15-puzzle. A cube ispacked withmarbles (in a gridarrangement), andone marble ismissing. By tippingthe cube themarbles can bescrambled and(hopefully!)unscrambled.

PatentNumber:


Square-1

Inventor(s): Karel Hrsel;Vojtech Kopsky


The canonicalSquare-1 patent.A simple dihedralmechanism letsthe central slabtrap any number ofappropriatelygrooved pieces oneither side.

PatentNumber:


Gerdig Ufo

Inventor(s): Gerhard HuncagaDate Filed: March 26, 1993Date Issued: December 6,

1994



PatentNumber:

HU207233PopularName:

Rubik's Triamid

Inventor(s): Ernoe Rubik;Emil Visnyovszky


PatentNumber:

US5199711PopularName:Inventor(s): Zoltan Pataki;

Geza Csomos;Janos Feher


A solid mechanismfor a puzzle slicedinto six radialsegments likeRubik's Cheese orthe Masterball.

PatentNumber:

RO106962PopularName:

Mad Marbles

Inventor(s): Florian RadutDate Issued: August 30, 1993

PatentNumber:


Massage Ball

Inventor(s): Otto WuDate Filed: October 28, 1993

PatentNumber:


Lights Out

Inventor(s): Revital Blumberg;Michael Ganor;Avish J. Weiner

Date Filed: April 8, 1994Date Issued: May 23, 1995



PatentNumber:


Switchback

Inventor(s): Ira FriedmanDate Filed: April 29, 1994Date Issued: August 1, 1995

PatentNumber:

RO110598PopularName:Inventor(s): Florian RadutDate Filed: June 14, 1994

Like the HungarianRings, this puzzlehas six interlockingrings of eightmarbles - the endresult is similar toa 3x3x3 cubewhere theorientation of thepieces doesn'tmatter.

PatentNumber:

US5338033PopularName:Inventor(s): Guillermo Nunez

SerranoDate Issued: August 16, 1994

An extremelysimple and elegant2x2x2 mechanism,nominally in aspherical puzzle.Each of the 7floating octantsclips into the axesand is held inplace by virtue ofthe shape.Contrast this withRubik's 2x2x2mechanism whichfalls apart whenany single piece isremoved.

PatentNumber:


Puzzle Ball

Inventor(s): Uwe MeffertDate Issued: October 25, 1994

The Puzzle Ball -a spherical Skewb.A four-armedspider withtriangular tips, fourmore floatingtriangular "faces",and six floatingsquare "faces".

PatentNumber:


Triple Cross





PatentNumber:

US5386993PopularName:Inventor(s): Bernardo H.

ApsanDate Issued: February 7, 1995

Another "Star ofDavid" - a 2x2x2mechanismembedded withinan octahedron,decorated withtrivially rotatingtetrahedra to forma stella octangula.

PatentNumber:


Lights Out 2000

Inventor(s): Avish J. Weiner;Avraham Y. Olti;Gyoray M. P.Benedek; MichaelGanor

Date Filed: May 5, 1995Date Issued: November 12,

1996

PatentNumber:


Orbix

Inventor(s): Uwe MeffertDate Filed: May 23, 1995

PatentNumber:


Lights Out

Inventor(s): Avraham Y. Olti;Gyoray M. P.Benedek; ZviHerman; RevitalBlumberg;Michael Ganor;Avish J. Weiner

Date Filed: January 18, 1996Date Issued: February 18,

1997

PatentNumber:


Astrolabacus

Inventor(s): John D. HarrisDate Filed: February 2, 1996



PatentNumber:


Puzzle Disc(Topspinvariation)

Inventor(s): Chiu-HuangChang


PatentNumber:


Puzzle disc(Super Top Spin)

Inventor(s): Chin-HuangChang



PatentNumber:


King Ring

Inventor(s): Zoltan Pataki;Istvan Varadi;Attila Kovacs

DateIssued:

March 21, 1996

PatentNumber:


Netblock Ufo

Inventor(s): Wai K. ChanDate Filed: April 15, 1996Date Issued: May 13, 1997

PatentNumber:


Mozaika

Inventor(s): Rudolf DesticsDate Issued: October 22, 1996

The Mozaikapuzzle. Theingeniouscombination of theEquator puzzle(three bands ofsquare on thesurface of asphere) with a2x2x2 mechanismallowing thecorners of thepuzzle to shiftposition.Appropriatecolorings of thepuzzle can varythe difficultysignificantly,



PatentNumber:


Brain Ball

Inventor(s): Andreas UnsickerDate Filed: February 4, 1997Date Issued: December 21,

1999

PatentNumber:


Inside Out(Vadasz Kocka)

Inventor(s): Daniel Ablonczy,Jozsef Vadasz

Date Filed: March 12, 1997Date Issued: January 12, 1999

PatentNumber:


Chromo Ball

Inventor(s): Tsun Ding ChenDate Filed: July 8, 1997

PatentNumber:


Eastsheen 2x2x2

Inventor(s): Chen Sen LiDate Filed: December 23,

1997Date Issued: October 27, 1998

PatentNumber:


2x2x2mechanism

Inventor(s): Chen Sen LiDate Filed: December 23,

1997Date Issued: October 27, 1998

This 2x2x2mechanismcontains acomplete 3x3x3mechanismincluding edgepieces, allconcealed by largecaps on thecorners. Puzzlesusing thismechanism havebeen found it isreportedly a greatimprovement overother 2x2x2mechanisms.



PatentNumber:

US5722657PopularName:Inventor(s): Dario CabreraDate Issued: March 3, 1998

An irregular 3x3x3variant. Each face-center has atrapezoidalprojection and thecorners aredegenerate. Theoverall appearanceis of threeintersectingwedge-shapedslabs.

PatentNumber:


Eastsheen 4x4x4

Inventor(s): Chen Sen LiDate Filed: March 25, 1998Date Issued: November 30,

1999

PatentNumber:


4x4x4mechanism

Inventor(s): Chen Sen LiDate Filed: March 25, 1998Date Issued: November 30,

1999

PatentNumber:


Eastsheen 5x5x5

Inventor(s): Chen Sen LiDate Filed: May 12, 1998Date Issued: October 10, 2000

PatentNumber:


5x5x5mechanism

Inventor(s): Chen Sen LiDate Filed: May 12, 1998Date Issued: October 10, 2000



PatentNumber:


Mad Triad

Inventor(s): Heng-Chun KuDate Filed: July 17, 1998Date Issued: February 8, 2000

PatentNumber:

HU214709PopularName:

Dogic

Inventor(s): Robert Vecsei;Zsolt Vecsei

Date Issued: July 28, 1998

PatentNumber:


Master Pyraminx

Inventor(s): Alexander MackDate Filed: October 15, 1998

An order-4tetrahedral puzzle,also known as theMaster Pyraminx(not an order-3Pyramix withrotating edges,which also goesby that name).The centralmechanism issimilar to a Skewb- a four armedspider with fourfixed triangularfaces (which formthe face-centers),four floatingtriangular faces(which connect tothe tips) and sixfloating squarefaces which arebuilt up intooctahedral "edge"pieces.

PatentNumber:


Maxim's puzzle

Inventor(s): John MaximDate Filed: July 9, 1999Date Issued: February 13,

2001



PatentNumber:


Display box forthe cube

Inventor(s): Sen-Li Chen(East SheenIndustrial Co.Ltd., TW)

Date Filed: January 4, 2000Date Issued: April 3, 2001

This redesign ofthe classic domedcontainer for the3x3x3 cube allowsthe cube to bepositioned eitherflat on one face,balanced along anedge, or balancedon a single vertex.

PatentNumber:


Dino Cube

Inventor(s): James R.Holloway


The canonicalDino Cubemechanism. Aninternal stellaoctangula'srotating tips havegrooves at thebase trap the outeredge pieces. Asimplified versionof Ashley'smechanism.

PatentNumber:


K-Ball

Inventor(s): Saleh KhoudaryDateIssued:

May 11, 2000

PatentNumber:

US6158740PopularName:Inventor(s): Albert J. HallDate Issued: December 12,

2000

A Dino Cubemechanism withmetal tippedpieces around acentral magneticcore, as well asgeneralizedpuzzles withmagnetic cores.

PatentNumber:


Darth Maul Cube

Inventor(s): Thomas KremerDate Issued: April 17, 2001

The Darth Maulcube; a 2x2x2mechanism similarto the one used inRubik's PocketCube™ but withaxis protrudingdirectly from thefixed octant, andembedded in abust of a popularcharacter.

NOTE: The information contained in this list should not be relied upon for reference purposes. Dates, names andnumbers may be incorrect. This information is provided with no warranty of any kind, express or implied.



* Why "magic polyhedra"? Rubik® is a trademark, and refers to Professor Ernö Rubik, inventor of a specific set of puzzles including the wildlypopular 3x3x3 cube that will forever bear his name. Similar puzzles created by other inventors should not be referred to as "Rubik's xyz" asthat is both a misuse of the trademark and a disservice to the hard work by these other inventors; as the above patents show, extending theconcept of a sliced polyhedron beyond the 3x3x3 cube is not trivial. A neutral name for this class of puzzles should be used instead. "MagicPolyhedra" and "Twisty Puzzles" are both in use to serve this role.

Rubik® and Rubik's Cube® are registered trademarks of Seven Towns Limited.

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