soma cubes - javamath.com · the seven pieces of cubes are named soma cubes. altogether you have...

What is a Soma Cube?

The seven pieces of cubes are named Soma cubes. Altogether you have 1x3 + 6x4 = 27 separate cubelets.

Main Problem top

Three solutions

All 240 solutions

Soma Cubes

Contents of this page What is a Soma Cube? Main Problem Positions of the Soma Pieces 3 and 2 Figures of Soma Cubes Magnification Problem

Making of Soma Cubes Three Variants: ...Soma schräg ...Chequered Pattern ...Coloured Cube

HistorySimilar Cube problems Soma Cubes on the Internet More 3x3x3-Puzzles References

To the Main Page "Mathematische Basteleien"

... ...

The main problem of the Soma "research" is to assemble the seven Soma pieces or 27 cubelets to make a 3x3x3 cube. The chance of solving this three-dimensional puzzle is good, because there are 240 possibilities to put the cube together, not counting symmetries.

If you try to solve the puzzle for the first time, you need approximately 15 min. You have a better chance if you start with the three-dimensional pieces 5,6,7.

1

... ...

2

...

3

...

Solution 1 was my first solution, which I kept in my mind. Solution 2 is easy to remember: You start with the three 3D pieces 5,6, and 7. Piece 4 follows. Solution 3 is one of the few solutions without piece 7 forming a corner.

Loesung Nr: 1

000 100 000 011 000 000 000 000 000 000 001 110 000 000 000 000 011 000 100 000 000

000 100 000 001 000 010 000

... ...

Jochen Wermuth makes available all 240 solutions found by a program in C++.

He is using the notation on the left.

The pattern has seven rows. The

페이지 1 / 9Soma Cube

2011-07-20http://www.mathematische-basteleien.de/somacube.htm

I offer all 240 solutions for downloading, likewise the source code in C++ with the author's agreement.

Positions of the Soma Pieces 3 and 2 top Piece 2 and 3 contain a 1x1x3 bar.

The shapes of the Soma cubes result in the following statements.

Piece 2 forms 0,1 or 2 corners. Piece 3 forms either 0 or 2 corners.

Now there are two possibilities: (1) Piece 3 forms no corners. The other six pieces form at most 2+5 corners. This case is not possible, because you don't have eight corners. (2) Piece 3 forms two corners. The other 6 pieces form 6 corners. Therefore piece 2 must form at least one corner.

Results:

This can be the first steps to prove that there are 240 solution.

Figures of Soma Cubes top

More well known figures are sofa, bed, bathtub, gate, gravestone, and tower.

000 110 001 000 000 000 000 000 000 001 000 000 000 110

000 000 000 000 000 111 000 111 000 000 000 000 000 000 100 000 000 000 000 000 011

whole cube and the position of a soma cube is given in a row.

The three blocks in the lines are assigned to the three layers on top, centre and bottom.

........ .. Piece 3 forms two corners.

Soma piece 2 must always form a corner and must not lie in the middle.

It is interesting to look for new 27-cubelet-shapes. This is one example, a "car".



There are innumerable figures of Soma cubes. This is proved by the following thoughts about designing new ones.

Two figures are insoluble.

Magnification Problem top Can you imitate a somacube with magnification? It is a productive problem with pentominos and tetracubes, but not with Soma cubes.

Making of Soma Cubes top

If you want to play with Soma cubes you have to construct them by hand.

The simpliest way is to buy a length of wood which is square in cross-section, cut it into cubes and glue the cubes together.

Another method is glueing dice. The best idea is to use a two component glue, because it needs time to harden. Then you can form the Soma pieces without having to hurry.

A cheap but difficult method is constructing them from a sheet of paper. You have to design the base of every Soma cube and fold it.

You can buy Soma cubes.

Parker Brothers sold the Soma cubes in 1969. Maybe they protected the name "Soma cube" by copyright.

In Germany you can buy them on Christmas fairs, mostly without a name or with other names like Ostfriesenwürfel ;-). Another version is Babylon. This is the "Rehmsche Spielsatz".

In the United States there is a game using Soma cubes, called Block by Block.

... ...

All Soma cubes have 27 cubelets. If you give a mat of 5x4 = 20 cubelets, there are [20 above 7] = 20!/13!/7! = 77520 places for the remaining seven cubelets, so 77520 figures. There is an example on the left.

... ...

If you form a bar with five cubelets, there are two left. So you get [15 above 2] =15!/13!/2! = 105 figures. There is an example on the left. If you demand symmetry, you only get 18 cube figures. You can see them as top view on the right and in perspective below.

... ...

... ...

Only the cube with three cubelets is possible. You need the rest of the Soma cubes to build it with double magnification.



Three variants

1st Variant: Soma schräg (Soma crooked) top There is a curiosity: You don't use a cube as the basic piece, but a parallelepiped. This is a figure bordered by parallelograms. In this case it is a rhombus with an 50° angle.

You should think you can simply apply the solutions of the 3x3x3 cube problem to this figure. You seldom succeed.

(Soma schräg, HOLZINSEL 56290 Beltheim, Art.-Nr. 019/1)

2nd Variant: Chequered Pattern top

You can produce this Soma puzzle, if you build a cube with method 2 and colour the cubelets black and white alternately. This pattern is transfered to the Soma pieces.

The problem is to form again a 3x3x3 cube of all pieces.

3rd Variant: Coloured Cube top

The problem is to form again a 3x3x3 cube of all pieces.

... ...

If you add three or four parallelepipeds, you get two possibilities of each Soma cube form. I only found one solution.

... ...

You can design new Soma puzzles, if you build a 3x3x3 cube and colour the surface all in one colour. You can also make a pattern (Example: die). The Soma pieces will adopt these changings, too.

If you like you can transfer these changings to inner squares in order to make the puzzle more difficult.



History top There are several forerunners of Soma Cubes. In 1936 the Dane Piet Hein took seven polycubes, so that they formed a 3x3x3-cube. There are ten pieces with 2,3, and 4 cubelets. He chose the polycubes, which don't form a cuboid.

Maybe he obtained the name from the book "Brave New World" by Aldous Huxley. Soma was the name of an addictive drug used in the fictional state in Huxley's book which is set in the year 2600.

Piet Hein (1905-1996) was a poet and scientist with wide ranging interests.

J.H. Conway and M.J.T. Guy worked out in 1961 that there are 240 possible ways to form a 3x3x3-cube. Computers confirmed this result later.

The Soma cubes became famous by its publication in the magazine Scientific American (1958). In Germany the magazine Bild der Wissenschaften circulated this puzzle (1967).

Similar Cube problems top Tetracubes Theodore Katsani suggested a game with all polycubes of four cubelets in the 1950s.

It is impossible to build a 3x3x3 cube, but 8*4=32 leads to cuboids 2x4x4 or 2x2x8 (4). You find more on my page tetracube.

Rehm's Cube Set There is the problem: Which polycubes with 3 or 4 cubelets form a 3x3x3 cube?

There are 14 possibilities for a 3x3x3 cube because of 27=3+6*4.

All sets except the combination II2..45678 (3 is missing) leads to a cube (5). The numbers inside the brackets is the number of solutions (Torsten Sillke, Rehm's 3-Cubes, URL below).

Hollow Cube

There are 2 tricubes and 8 tetracubes. ... The numbers are used in book 5.

I345678 (138)

I245678 (000)

I235678 (031)

I234678 (099)

I234578 (245)

I234568 (245)

I234567 (027)

II345678 (240)

Somawürfel

II245678 (047)

II235678 (261)

II234678 (221)

II234578 (337)

II234568 (337)

II234567 (039)

You can build a hollow cube from the tricubes I and II and the tetracubes



You can ask for more solutions with other tetracubes of Rehm's cube set and for the number of solutions. (This idea had Volker Latussek from Würzburg.)

More 3x3x3-Puzzles top All soma cubes together contain 27 cubelets. The distribution is 27=3+4+4+4+4+4+4.

You can imagine that there are more sums between 27=1+1+...+1 and 27=9+9+9, which are suitable for puzzles.

I introduce some puzzles in this chapter, which I found more at random. [There is more systematic on the pages of David Singmaster, Stewart T. Coffin und Erich Friedman (URL below).]

Diabolical Cube - Hoffmann (27=2+3+4+5+6+7)

Mikusinski's Cube (27=4+4+4+5+5+5)

Der vertrackte Würfel- The tricky cube (27=4+4+4+5+5+5), "Toys pure", Art.-Nr.:HS 630

Loops cube (27=4+4+4+5+5+5), designed and made by René Dawir

... ...

3,4,6,7 and 8. There is 2*3+5*4=26

...

...some solvable symmetric figures

...

There are two solutions only.

...I only found a 4x5 mat with 7 cubelets on top, which is worth to show, after playing around.

...

...

You can form a closed ring with all pieces.



Soma Cube on the Internet top German

C. Meier - Warenhandel Holzwürfel - Somawürfel - Dezimalrechenwürfel

http://www.zahlenjagd.at/ Würfelpuzzles

Matroid Matheplanet Der Soma Würfel

Peter Kenter (Mathematik und Kunst) Die 41 Polykuben der Ordnung 1 bis 5 (pdf.-Datei)

Stromberg-Gymnasium, Vaihingen an der Enz Der Somawürfel

Wikipedia Somawürfel

English

asahi-net.or.jp/~rh5k-isn 3x3x3 Cube Puzzles

Balmoral Software Soma Site

Bill McKeeman Soma Cube Solutions

Binary Arts Corporation (Binary Arts' Block by Block® puzzle) Millennium Puzzles: Soma cube

...

Order in the solution: 564321



Christian Eggermont The Soma Cube ("Go to the puzzles!")

Courtney McFarren (Mathematica) The Soma Cube

David Singmaster CLASSIFICATION OF DISSECTED CUBES (.doc file)

Erich Friedman Erich's 3-D Jigsaw Puzzles

Lee Stemkoski (Mathematrix) The Soma Cube

Thorleif Bungård Thorleif's SOMA page

Torsten Sillke cube-secrets , Rehm's 3-Cubes (1980)

Wikipedia Soma cube, Bedlam cube, Conway puzzle

Youtube SOMA CUBE puzzle solution, Puzzle Cube Solution, How to solve the Bedlam Cube Retro

References top (1) "Bild der Wissenschaft" November 1967 (2) Pieter van Delft /Jack Botermans: Denkspiele der Welt, München 1980 (1998 neu aufgelegt) [ISBN 3-685-1998) (3) Martin Gardner: Bacons Geheimnis, Frankfurt am Main, 1986 [ISBN 3-8105-0800-

Ed Vogel A very large Soma puzzle at the Minnesota State Fair 2006



4] Fast 30 Jahre nach Erscheinen einer Kolumne in der Septemberausgabe 1958 von <Scientific American> zieht der Autor eine Bilanz der "Somaforschung". (4) R.Thiele, K.Haase: Der verzauberte Raum, Leipzig, 1991 [ISBN3-332-00480-8] (5) R.Thiele, K.Haase: Teufelsspiele, Leipzig, 1991 [ISBN 3-332-00116-7]

Feedback: Email address on my main page

This page is also available in German.

URL of my Homepage: http://www.mathematische-basteleien.de/

© 1999 Jürgen Köller top



BASIC SOMA figure page

This initial group of figures was presented in the original SOMA manual.

The basic 7 shapes

SOMA figures

A001 THE CUBE N001 Step2 P001 Cube parts

P002 Double 1

P003 2*1/2CUBE

A002 aeroplane A003 dog A004 robot

A005 crystal A006 castle 1 A007 bed A008 tower

A009 chair A010 bathtub A011 castle 2 A012 snake

페이지 1 / 12Soma figures #1

2011-07-20http://www.fam-bundgaard.dk/SOMA/SOMA1/SOMAFIG1.HTM

A013 tunnel A014 gallow A015 cornerstone

A016 sofa

A017 steamer A018 well A019 monument A020 tomb

A021 cornerhouse 1

A022 cornerhouse 2

A023 gordian knot

A024 memorial

A025 pyramid A026 staircase A027 skyscraper1

A028 skyscraper2

A029 skyscraper 3

A030 appartment block 1

A031 appartment block 2

A032 zig zag wall



The SOMA Solutions in this window show the figures as each level is sliced,

from the top and down. The method is described on the "Figure Notation method" page. http://www.fam-bundgaard.dk/SOMA/FIGURES/NOTATION.HTM Try to build the figures above, and then click on the name of the figure when you need to see it's description.

A001 The final cube

4 theoretical positions of block no 7. Which of these are possible ? (7A Yes) (7B No) (7C Yes) (7D No)

A033 'W' wall A034 High & low 1

A035 High & low 2

A036 5 seat bench

2 2 6 4 6 6 3 3 3 5 2 1 4 6 1 4 3 7 Solution 1 5 2 1 5 5 7 4 7 7 2 2 3 4 2 5 4 2 5 4 6 3 4 6 3 7 5 5 Solution 2 (Figure)6 6 3 7 1 1 7 7 1

4 5 2 7 5 5 7 7 6 4 1 2 4 6 5 7 6 6 Solution 3 (Figure)1 1 2 4 3 2 3 3 3 1 5 3 7 5 2 7 7 2 1 1 3 5 5 3 7 6 2 Solution 4 4 4 3 6 4 4 6 6 2

3 1 1 3 3 7 3 4 4 6 1 2 5 7 7 4 4 7 Solution 5 (Figure) 6 6 2 5 6 2 5 5 2 1 6 6 4 4 6 2 4 4 Solution 6 (Used by 'Block by Block') 1 1 7 3 5 6 2 2 2 3 7 7 3 5 7 3 5 5



N001 Soma looks easy, but even if you use only 2 blocks difficult shapes can be made: this figure can be made of 2 blocks. which and how ?

P001 (Soma pairs 1) If you start with the previous shape, it will be particularly difficult to build the cube

P002 Double size (Soma pairs 2) If the smallest block (No 1) is removed, you may build a double size of it, using the remaining blocks. This looks easy.

P003 The cube in halves (Soma pairs 3) by Piet There is a special way of building the cube, First build the two shapes, and then combine then to the cube

A002 The Aeroplane

2 2 2 . 6 . 6 6 2 . 6 .

. . 2 2 | 3 . . 3 1 1 3 4 16 6 2 6 | 5 . . 3 . . 4 4 7. . 2 6 | 5 . . 5 5 7 4 7 7

1 1 7 2 6 6 7 7 4 61 3 2 2 2 7 4 4 6 3 3 5 4 3 5 5 5

2 2 . 4 2 5 4 2 5 4 . . 4 . . 7 5 5 . . . 7 . . 7 7 . 2 2 3 4 2 5 4 2 5 + = 4 6 3 4 6 3 7 5 51 . . 1 3 . 3 3 3 6 6 3 7 1 1 7 7 1. . . 1 6 . 6 6 . . . . . . . 6 . .

5 . 5 5 5 1 1 1 4 4 3 3 3 . 2 7 4 4 3 2 2 27 7 7 6 6 6 6 .



A003 The Dog

A004 The robot

A005 The crystal

A006 The castle 1 by Piet

A007 The bed

. . . . . . . . . . . 7 . . . 7 7 4 4 5

. 1 2 . . . 1 1 2 . . . . 6 2 2 5 5 . 7 4 4 3 5

. . . . . . . . . . . 6 . . . 6 6 3 3 3

7 7 7 7 . . . . . 1 1 2 2 2 . . . 1 2 3 . . . 4 3 3 . . . 4 4 3 . . . 6 4 5 6 . . 5 6 6 5 5

7 . . 7 7 . 4 6 6 4 4 6 3 4 2. . . 7 . . 5 5 . 1 5 6 3 3 2. . . . . . 5 . . 1 1 . 3 2 2

6 . . . 5 6 3 3 3 5. . . . . 6 6 3 5 5. . . . . 4 4 2 2 2. . . . . 7 4 4 1 27 . . . 7 7 1 1

7 . . . . . 6 7 7 3 3 3 6 65 . . . . . 1 7 4 4 3 2 6 15 . . . . . 1 5 5 4 4 2 2 2



A008 The tower (Try to leave out 1 block to make it 1 story smaller. (No 6))

A009 The chair

A010 The bathtub

A011 The castle 2

A012 The snake

6 6 2 2 4 2 4 2 5 5 1 1 7 16 . 6 3 3 3 4 3 4 5 7 5 7 7

3 2 2 3 3 2 3 4 2 7 4 4 7 7 4. . . . . . . . . 6 6 5 7 1 1. . . . . . . . . 6 5 5 6 5 1

2 2 2 7 7 5 5 2 3 75 . . . 7 5 6 3 3 36 4 4 1 1 6 6 4 4 1

6 . . . 5 6 3 3 3 5. . . . . 6 6 3 5 5 . . . 1 4 4 . . . . . 7 1 1 4 47 . . . 2 7 7 2 2 2

2 2 . . . 2 . . . 2 4 4 . 4 4 6 . . . . . . 6 6 5 6 5 5 . . . . . . 5 3 7 3 3 3 . . . . . . 7 7 1 7 1 1



A013 The tunnel

A014 The gallow

A015 The cornerstone

A016 The sofa

. 4 4 3 . . 6 . 3 . 6 6 . 3 1

. 7 4 4 . . 5 . 3 . 6 5 . 1 1

. 7 7 2 . . 7 . 2 . 5 5 . 2 2

Alternative

. . . . . . . . . . . . 1 7 5 1 5 5

. 2 . . 2 . . 2 . . 7 . 7 7 5 1 6 6

. 2 . . . . . . . . 4 . 4 4 6 4 3 6 . . . . 3 3 . . . . . 3

Alternative

7 . . . . 7 7 . . . 2 5 5 . . 2 5 6 1 . 4 6 6 1 1 . . 7 . 2 . 4 5 4 6 . . 2 4 3 . . . 3 3 . . . . 3



A017 The steamer

A018 The well

A019 The monument

A020 The tomb

A021 The cornerhouse 1

3 3 3 4 4 2 3 4 4 6 2 2 2 6 6. . . . . 7 . . . 5 7 7 1 6 5. . . . . . . . . . 7 1 1 5 5

. . . . . . 6 6 1

. . . . . 6 7 . 5 6 1 1

. . 7 . . . 5 7 7 . 5 5 3 3 3 . . . . . 4 4 . 4 4 3 2 . . . . . . 2 2 2

1 2 2 1 6 2 6 6 21 . 7 3 . 5 6 . 53 7 7 3 4 7 3 5 5 . 4 4 . . 4

2 . . . . 2 . . . . 2 3 5 1 . 3 3 3 1 1. . . . . . . . 2 6 5 . 6 6 5 5 . . . . . . 4 7 . 6 7 7 . . . . 4 . 4 7 . . . 4

. 3 . 3 3 3 . 2 . . 2 . 7 2 1 7 7 1

. . . . . . . . . . . . 5 2 1 7 6 6

. . . . . . . . . . . . 5 4 6 5 5 6 . . . . 4 4 . . . . . 4

4 2 2 4 4 2 6 4 2 6 6 31 1 . 5 5 . 6 5 . 7 3 31 . . 5 . . 7 . . 7 7 3



A022 The cornerhouse 2

A023 The gordian knot

A024 The memorial (Proven impossible)

A025 The pyramid

A026 The staircase

1 7 . 1 7 7 4 5 5 2 3 5 3 3 31 . 4 7 4 5 2 6 6 6 . 4 2 2 6

. . 6 . 4 . 6 4 4 6 6 4 . 5 5 2 . . 5 7 2 . 3 3 3 2 2 . 7 . 5 7 7 3 1 1 . . 1

. . . . . . 2 2 2 . . . . . . . 7 . . 3 2 5 1 1. . 7 . . . 7 7 5 . 3 3 5 5 1. . . . . . . 6 . . 3 6 6 4 4 . . . . . . 6 4 4

. . 3 . . . 3 3 4 . 1 1 3 2 2

. . 5 . . . 6 7 4 . 1 7 7 4 2

. . 5 . . . 6 5 5 . 6 6 7 4 2



A027 The skyscraper 1

A028 The skyscraper 2

A029 The skyscraper 3(Is it possible ?)

A030 The appartment block 1

A031 The appartment block 2

. 2 . . 2 . 1 2 . 1 1 . 7 7 . 7 3 . 3 3 3

. . . . . . 4 2 . 4 4 . 7 4 . 6 5 . 6 5 5

. . . . . . . . . . . . . . . . . . 6 6 5

. . . . . . 1 4 . 1 4 . 7 7 . 7 5 . 3 5 5

. 2 . . 2 . 2 2 . 1 4 . 7 4 . 3 6 . 3 6 5

. . . . . . . . . . . . . . . . . . 3 6 6

6 1 1 4 4 1 7 4 4 3 6 6 5 7 6 5 7 7 3 3 3 2 2 2 5 5 2

6 2 2 6 6 2 5 5 2 4 4 6 1 1 5 7 1 5 3 4 4 3 3 7 3 7 7



A032 The zig zag wall

A033 The 'W' wall(is it possible ?) (I can't do it - see my almost figure)

A034 High and low 1

A035 High and low 2

A036 The five seat bench

6 1 1 1 4 4 2 6 6 6 4 4 7 2 5 2 5 2 7 7 3 7 5 5 3 3 3

.

. . . 3 3 37 4 4 . . . 7 7 4 4 3 25 1 1 . . . 7 6 6 2 2 25 1 6 5 5 6

. . . 2 2 2 . . . 4 4 27 7 3 . . . 7 3 3 3 4 47 5 5 6 1 1 6 6 5 6 1 5

4 7 7 7 4 4 . 1 1 7 6 4 . 6 6 1 2 6 . 2 2 2 5 3 . 3 3 3 5 . 5 5



The SOMA figures on this WEB-SITE are arranged in short .HTM files, each file contain: One image (with max. 25 figures) and a text describing the solutions.

If you have the Bundgård & McFarren SOLVE program, you may save the .HTM pages holding solution texts, in the directory where you have SOLVE, and then load them into SOLVE to investigate the figures further.

How do we write SOMA solutions ?

A lot of people are playing with the SOMA and SOMAplus puzzles, and once in a while - the question arises. We have made a figure but how do we write the solution on paper.

Now there are several ways to write down a puzzle.

We could draw the figure and color the pieces. We could draw the figure in slices. We could give every piece a number and write the figure in text.

I have chosen the last solution. and all figures on these SOMA pages, have their solution described in a LETTER notation.

This is how the notation works.

First we give each piece a number, or a letter. You may ask why a number AND a letter, well the initial way was to use a number but then several people made puzzles using two SOMA sets, and to separate the pieces, the pieces of the second set was given letters as codes. Finally the introduction of the SOMAplus puzzle added more letters.

SOMA.

SO. the SOMA pieces are named 1,2,3,4,5,6,7 or V,L,T,Z,A,B,P

Notation for SOMA Figures E-Mail.

The first 36 figures do also have an especially thorough describtion, if you follow the path. / ALL SOMA Figure images / 0001-0036

페이지 1 / 4Notation for SOMA Figures

2011-07-20http://www.fam-bundgaard.dk/SOMA/FIGURES/NOTATION.HTM

I know it is confusing to have both a number AND a letter for a piece, but it DO help when writing down figures, and if you are using just a single SOMA set (As most people do) then you can chose yourself to use numbers or letters.

Now to solve a SOMA puzzle, you must read the solution code for the puzzle. Let's examine the figure number 007 "THE BED"

The solution looks like this

/SOMA007 /7.....6/7733366 /5.....1/7443261 /5.....1/5544222

The first line is simply the identification /SOMA007 The '/' is used by our SOLVER software, and is a separation character The next lines show the figure seen from the top, as slices of cubes. The top slice is at the left. So if we expand it a bit, and remove the '/', it gets easier to see.

/SOMA007 7.....6 7733366 5.....1 7443261 5.....1 5544222

If you look at the bottom layer (to the right), look at the first line, you see the number '3', this is the 'T' shaped piece laying flat, To the left of this you see the number '7', which is the pyramid shaped piece, and if you look at the left side drawing, you see that this piece no.7 extend one of its cubes into the top layer.

Try to put this puzzle together, and you get the BED

The notation contain a few definitions. Used by the SOLVER software. You don't have to be strict on this unless you are writing your data for the SOLVER program. A figure starts with /SOMA and a number or name. Numbers are 000-999, Capital letters are also allowed, so BI01 is also a valid name, written as /SOMABI01 A figure comment starts with ; A figure description starts with / Cubes are named 1,2,3,4,5,6,7 or V,L,T,Z,A,B,P Empty cells are written as 0 or . or - There MUST be an empty line after a figure. NO other lines are allowed inside a figure description. Any text may be written in all the other lines.



SOMAplus.

When we talk about the SOMAplus pieces I call them 0,1,2,3,4,5,6,7,8,9,$ or D,V,L,T,Z,A,B,P,I,Q,S For this description I have also attached a color to each piece, so that it is easier to see the pieces in the drawings.

Now lets examine the basic SOMAplus 2x4x5 box. First in the notation:

And then in drawings:

SO - If you have a SOMAplus set, you could make this figure too.

I have 3 ways of grouping the figures.

All Figure images I group in sections like 'General, Bundgaard' etc. This is simply a logic way, holding contributions, including your's, in the first groups. Bundgård are my and my family's figures. Other named groups come from people who have produced large sets of new figures.

ALL new figures are added to the list at the rate that I find, receive or make the figures. The system is sequential. Each group is starting at 001.

NONOMINOES

/SOMAplus 001 ;The 2,4,5 Base /AABSS/ABBVV /TTTSS/ABDZV /PTLLL/PPDZZ /QQQQL/PIIIZ

=> Identifying the figure => The name of the figure => /Top Slice rear /Bottom slice rear => / / => / / => /Top Slice front/Bottom slice front

Nonominoes are any figure that is made of 9 columns of 3 cubes each. Here we see the original Piet Hein figures 031 and 032. These two, and a few more from the original sets, are NONOMINOES for example. The Cube(000) the Bed(007) the chair(009) and the bridge(013) are all NONOMINOES, they are just lying on their side. So, you see that the NONOMINOES cover many known figures, even the famous 'W-Wall' ALL 1069 SOMA-NONOMINOES are listed in this 1999.03.08 Newsletter.



Browse ALL Images here. This is an easy way to jump around among the many figure drawings, without having to load their solutions.

Here's a hint

Written by Thorleif Bundgaard.

If you too have trouble remembering which one is no 5 and which is no 6, then use my rules of thumb's; The figures have shapes like hands, and we read from left to right, so count left=5 and right=6. Using letters, then remember A is before B. Of course if you are Arab or chinese, who read from other directions, you have to use some other rule.



Overview of Soma Puzzles

If you want to submit your own constructions, please use e-mail. Enjoy

페이지 1 / 3Overview of Soma Puzzles

2011-07-20http://web.inter.nl.net/users/C.Eggermont/Puzzels/Soma/overzicht.html

Author: Christian Eggermont Created: 28 July 1997 Last updated: 1 Augustus 1997



soma cubes - javamath.com · the seven pieces of cubes are named soma cubes. altogether you have...

Documents