索馬立方體(Soma Cube)是 Piet Hein 於 1936 年發明的實體智力拼塊遊戲，將
七個由 1×1×1 立方體製成的立體組裝成 3×3×3 的立方體。在 1961 年時，索馬立
方體的 240 種不同的解（鏡像解視為相同）第一次由 John H. Conway 和 Michael
J. T. Guy 列出，但當時手稿 SOMAP 是很難理解的。
此篇論文的目的是通過找到 10 種基本分類的方式將解轉化為適合探索的數
學實驗。透過這些基本分類的方式所找到的解法，可以繼續延伸出其他新的解
法。由於數學發現往往伴隨著對稱性，在這篇論文中我們列出 5 對在過程中對稱
的例子作為索馬立方體的解法。
此篇論文的應用層面包含了：如何將索馬立方體融入教學中，透過讓學生動
手實踐和討論，提高數學興趣和思維能力。並在最後草擬了在數學競賽和科展的
一些標題。

The Soma cube is a solid dissection puzzle invented by Piet Hein in 1936, in which seven pieces made out of unit cubes must be assembled into a 3×3×3 cube. The total number of solutions (240) was first enumerated by John H. Conway and Michael J. T. Guy in 1961. The logic behind the enumeration was crafted with SOMAP which is hard to understand. The purpose of this thesis is to convert the puzzle into a mathematical experiment suitable for elementary exploration by finding 10 essential dissections. Once the essential solutions are found we may proceed to discover other new dissections. Since mathematical discoveries are often accompanied by consideration of symmetries, we are to list 5 pairs of such examples. As applications will to discuss how Soma Cube can be integrated into the teaching, so that students hands-on and through discussion, to enhance the mathematical interest and thinking ability. A program to forester innovative thinking both in mathematics competition and in science fair is drafted.

Contents
1. Introduction……………………………………………………………1
1.1 Soma Cube…………………………………………………………..….………1
1.2 The Possible Positions of Seven Pieces…………………………………………2
1.2.1 Possible positions of Piece 3…………………………………….…..……2
1.2.2 Possible positions of Piece 2……………………………….………..……3
1.2.3 Possible positions of Piece 1 and Piece 7…………………………………3
2. Essential Soma Cubes………………………………….………………4
3. Symmetry in the process……………………………….………………9
4. Extension of 10 Essential Soma Cubes……………………………….11
5. Application in Education…………………………………..…….……16
5.1 A program in Soma Cube exploration…………………………………………17
5.2 Application of Soma Cube in Mathematics Competition and Science Fair…...18
5.2.1 Application of Soma Cube in Mathematics Competition………………..18
5.2.2 Application of Soma Cube in Science Fair…………………….………..18
6. Reference………………………………………………………...…….………..18

[1] E.R. Berlekamp, J.H. Conway and Richard K. Guy, Winning Ways for your Mathematical Plays, Volume 2: Games in Particular (Academic Press, New York,
1982), p.735-739,802-803
[2] Christoph PETER-ORTH, All solutions of the Soma Cube puzzle., Discrete Mathematics, 57 (North-Holland, 1985), p.105-p.121
[3] M. Gardner, The 2nd Scientific American Book of Mathematical Puzzles & Diversions (Simon and Schuster, New York, 1961), p65-p77
[4] Richard K. Guy, John Horton Conway: Mathematical Magus, The Two-Year College Mathematics Journal, Vol. 13, No. 5 (Mathematical Association of America Stable,Nov., 1982), pp. 290-299,
URL: http://www.jstor.org/stable/3026500
[5] Richard K. Guy and Marc M. Paulhus, Nine Cubits or Simple Soma, The College Mathematics Journal, Vol. 33, No. 3 (Mathematical Association of America Stable,
May, 2002), pp. 188-195, URL: http://www.jstor.org/stable/1559027
[6] 楊淑貞（2012）。 從索瑪立方塊看做中學的教學意義。輔導員落實數學課室
教學之經驗分享篇 12，p155-p172。彰化縣
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中華民國第 55 屆中小學科學展覽會，國中數學組
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http://www.chiuchang.com.tw/toy/somacube.html
[10] Soma Cube
http://www.mathematische-basteleien.de/somacube.htm#History
[11] Soma Figures
https://www.fam-bundgaard.dk/SOMA/FIGURES/FIGURES.HTM
[12] Polycubes: Puzzles & Solutions
http://puzzler.sourceforge.net/docs/polycubes.html#soma-cubes
[13] 全國中小學科學展覽會─國立台灣科學校育館
https://twsf.ntsec.gov.tw/Article.aspx?a=41&lang=1
[14] 博士兒實業有限公司(USL 連接方塊)
http://child.mymy.tw/item-appraisals.html?&id=39363