SOMA Crystal
SOMA News 9 may 2016 plus: 24 june 2016

A way to solve the SOMAP.

Another story from Merv Eberhardt.
Newsletter 2015.10.08   The Normalization of SOMA solutions, by Merv Eberhardt.
And the lead story from William Kustes.
Newsletter 2003.05.18   The complete "SOMAP" is found by William Kustes.

Merv Eberhardt worked hard at the folding and shifting details involved in the SOMAP.

Merv wrote to me again on 2016-04-25, that,
Since my efforts to translate (normalized position) the 240 solutions~
as listed in the SOMA Newsletter 1 Feb 1999 (N990201 "Winning Ways for your mathematical plays")
and were published as 2015.10.08 ("The Normalization of SOMA solutions."),
I put my efforts on the back burner, so to speak.
About a month ago I've started an investigation of the SOMAP.
It is really a masterpiece of elegant detail.
First of all I noticed that there are only 239 solutions shown on the SOMAP.
In any case, through studies of the various translations, I've been identifying about 114 of the two-piece translations.
My next step is to match them against the published solutions.

Yours Truly,
Merv Eberhardt

So - Here is his own story about ....

How I Solved the SOMAP by Merv Eberhardt of Huntsville, Alabama.

This article is intended for the many readers of the SOMA newsletter that are passionate about the SOMA phenomena
and the brilliance of the SOMAP. I am dispensing with many necessary details so that I can focus on my efforts that led to my discovery of the solution to the SOMAP.

I refer the reader to the basic references at the end of this article that are critical to the background,
history, and nomenclature of the SOMA puzzle and to the SOMAP.

The key topics are: SOMA creation by Piet Hien; description of the seven SOMA pieces; makeup of the SOMA cube (i.e. faces, edges, vertices, and center); 240 SOMA cube solutions by hand by John H. Conway and Richard K. Guy; SOMAP discovery by John H. Conway; SOMATYPE (i.e., deficiency, centrality, and dexterity); and the hidden secrets of SOMA (i.e. piece #3/Green must be along an edge in FEVV orientation in every solution).

This entire effort was based on reverse engineering of the seven SOMA pieces to achieve the designated SOMAP cube codes (the SOMATYPE) as presented in the SOMAP.

My initial interest in the SOMAP focused on the "genesis" nodes. Those were the ones with the "a" sequence designation, i.e., A0a, RU4a, U2a, etc. I also noticed the 14 gy-go-oy transitions throughout the SOMAP. The sequence RU2b<gy>RU4a<go>RU2a at the bottom of the SOMAP was where I began.

So, starting with the <oy> translation between layouts RU4a and RU2a, I recognized that the RU2a layout required a dexterity of 2 to be satisfied by the Yellow (#2 / L shape) piece and that the RU4a layout would require a dexterity of 4 to be satisfied by the Orange (#4 / Z shape) piece. I determined that the following layout on the bottom layer would provide the proper transition and dexterity values.
Please note that the dexterity positions (values) are to be viewed by looking at the bottom of the bottom layer.

    RU4a     RU2a
B  Y Y Y    Y Y O
O  Y O O<oy>Y O O
T  O O x    Y O x
The next consideration was the <go> transition from the RU4a to RU0a. This would add the Green (#3 / T shape) piece in the two initial layouts. The piece would not influence the dexterity by itself but the transition would require the O piece to change its dexterity from 4 to 0. It was somewhat obvious that one of the ends of the G piece would occupy the remaining space in the bottom layer; but its orientation in the middle and top layers was to be determined, as well as how it would be positioned in the RU4a and RU2a layouts.
This lead to the following:
T  x x x    x x x    x x x
O  x x x    x x x    x x x
P  x x O    x x G    x x G
    RU0a     RU4a     RU2a 
M  x x x    x x x    x x x
I  x x O<go>x x G<oy>x x G
D  x x O    x x G    x x G
B  Y Y Y    Y Y Y    Y Y O
O  Y G O    Y O O    Y O O
T  G G G    O O G    Y O G
The <gy> transition from RU0a to RU2b was straightforward.
The G and Y pieces would exchange positions in an obvious way such that the dexterity of the Y piece would change from 0 to 2 (reverse its dexterity).
The result is:
T  x x x    x x x    x x x    x x x
O  x x x    x x x    x x x    x x x
P  x x O    x x O    x x G    x x G
    RU2b     RU0a     RU4a     RU2a
M  x x x    x x x    x x x    x x x
I  x x O<gy>x x O<go>x x G<oy>x x G
D  x x O    x x O    x x G    x x G

B  G G G    Y Y Y    Y Y Y    Y Y O
O  Y G O    Y G O    Y O O    Y O O
T  Y Y Y    G G G    O O G    Y O G
Be aware that the three pieces (i.e., O, Y, and G) that make up these four layouts occupy five of the eight cube corners (vertices).

To complete these basic four layouts the orientation of the remaining four pieces: i.e. A (#7/Y shape/ blAck), B (#1/ V shape/ Brown), R (#6/ Right Twist shape/ Red), and U (#5/ Left Twist shape/ blUe), must be determined.
The following criteria must be met: piece R must be deficient, that is it must not occupy any of the remaining three cube corners, piece U must occupy the center space of the cube and must occupy a cube corner, and pieces B and U must each occupy a cube corner. And the B piece must not add to the dexterity.

The resulting complete layouts are as follows:
T  A A B    A A B    A A B    A A B
O  A R R    A R R    A R R    A R R
P  U R O    U R O    U R G    U R G
    RU2b     RU0a     RU4a     RU2a
M  A B B    A B B    A B B    A B B
I  U U O<gy>U U O<go>U U G<oy>U U G
D  U R O    U R O    U R G    U R G

B  G G G    Y Y Y    Y Y Y    Y Y O
O  Y G O    Y G O    Y O O    Y O O
T  Y Y Y    G G G    O O G    Y O G
With the identification of these three swaps (gy-go-oy) of the four layouts (RU2b-RU0a-RU4a-RU2a), all of the remaining SOMAP cube codes can be revealed from the specified two and three piece swaps.

Immediate attention can be given to the <ru> swaps to form the U2b-U0a-U4a-U2a layouts. Pieces R and U are swapped such that piece U continues to occupy the center position and must switch with piece R in occupying a corner position.
In SOMATYPE terminology, piece U must become both deficient and center.

I must admit that the positioning of the four B, U, R, and A pieces might seem a bit arbitrary, (while following the deficiency, centrality, and dexterity constraints).
My two personal criteria were: positioning the A piece in the top, back, left position and the B piece to be readily positioned to meet the <bg> transition from RU2b to RU2c

I would like to point out several challenges that appear on the SOMAP.
They consist of 23 three-way patterns that consist of swaps between <ab>, <br>, <bu>, and <roy>. And a swap <guy> between four solutions. These must take into account the differences between the three variables of cube codes, i.e. deficiency, center, and dexterity. A true test of SOMAPmanship.

Good luck. Let me know of your success.

SOMA / SOMAP References:

The complete "SOMAP" is Found”, SOMA Newsletter, 18 March 2003.

A Living SOMA Classic (the SOMAP), SOMA Addict Newsletter, 1972, (Vol 2. No 2. Page 2.)

Winning Way's About the SOMA Cube Solutions, , SOMA Newsletter, 1 February 1999.

Winning Ways About Your Mathematical Plays, Volume 2: Games in particular,
    Elwyn R. Berlekamp, John H. Conway, Richard K. Guy,
    Academic Press. ISBN: 0-12-091102-7, Chapter 24 (Page 735) ?Pursuing Puzzles Purposefully.

Now 2016-06-24 Merv Eberhardt wrote a commentary letter. Which I will let you read here:

Fellow SOMA Addicts,

Recently I've analyzed the SOMATYPEs of the SOMA solutions as listed in the SOMA Newsletter, 1 Feb 1999 against those of the SOMAP.
The results confirmed my most negative feelings.

Since I've successfully navigated the SOMAP, I've been interested in mapping those 240 double/triple swaps that were so brilliantly discovered and depicted in the Conway-Guy masterpiece into the incredible revelation of the 240 possible solutions of the SOMA Cube Puzzle.
It's confirmed, the majority of the 240 SOMA solutions are reflections of the SOMAP solutions.

Case 1: There are 64 RU and 1 UR SOMATYPEs on the SOMAP.
There are 34 RU and 31 UR SOMATYPEs in the 240 SOMA solutions.
The combined solutions are 61.

Case 2: There are 13 R and 38 U SOMATYPEs on the SOMAP.
There are 26 R and 25 U SOMATYPEs in the 240 SOMA solutions.
The combined solutions are 51.

There are also many differences with dexterity values that point to reflections.

I recall asking about the SOMA Newsletter solutions over a year ago.
It was stated that they were the result of some computer program.
Thorleif's note:
The 240 solutions presented in the 1999-02-01 SOMA Newsletter were found using the program made by Sivy Farhi, described in the 1999-01-21 SOMA Newsletter

Well it seems that my SOMAP results are what was often stated,
"The complete list of 240 SOMA solutions was made by hand ... one particularly rainy afternoon in 1961."
Again, I'm assuming that those historical discoveries are what Conway and Guy included in the SOMAP. Their admonition that use of a computer was an "admission of defeat."

I'll now cease to try to find the SOMAP solutions amongst the SOMA Newsletter solutions.
I have found the "holy grail" of SOMAP solutions and now I can rest in peace.

Merv Eberhardt.

Written by Merv Eberhardt. <>
Adjusted by Thorleif Bundgaard <>

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