# 多連立方體

## 多連立方體的列舉

n 多連立方體的名稱 不考慮鏡對稱 考慮鏡對稱
1 單立方體
monocube
1 1
2 雙立方體
dicube
1 1
3 三連立方體
tricube
2 2
4 四連立方體
tetracube
8 7
5 五連立方體
pentacube
29 23
6 六連立方體
hexacube
166 112
7 七連立方體
heptacube
1023 607
8 八連立方體
octocube
6922 3811

## 五連立方體

12個平面的五連立方體與五格骨牌相互對應。其餘17個五連立方體中，5個具有鏡像對稱性，另外12個形成6組手性對。

## 參考資料

1. ^ Weisstein, Eric W. (编). Polycube. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. [2016-07-27]. （原始内容存档于2017-06-29） （英语）.
2. Lunnon, W. F., Symmetry of Cubical and General Polyominoes, Read, Ronald C. (编), Graph Theory and Computing, New York: Academic Press: 101–108, 1972, ISBN 978-1-48325-512-5
3. ^ Polycubes, at The Poly Pages. recmath.org. [2022-08-12]. （原始内容存档于2021-07-25）.
4. ^ Kevin Gong's enumeration of polycubes. [2022-08-12]. （原始内容存档于2013-09-04）.
5. ^ . "Pentacube". From MathWorld. [2022-08-13]. （原始内容存档于2019-09-08）.
6. ^ Theoni Pappas, 陳以鴻譯. 《數學放輕鬆》. 臺北縣新店市: 世茂出版社. 2004. ISBN 9577766110.
7. ^ Kemp, Martin, Dali's dimensions, Nature, 1 January 1998, 391 (27): 27, Bibcode:1998Natur.391...27K,
8. ^ Fowler, David, Mathematics in Science Fiction: Mathematics as Science Fiction, World Literature Today, 2010, 84 (3): 48–52, JSTOR 27871086, Robert Heinlein's "And He Built a Crooked House," published in 1940, and Martin Gardner's "The No-Sided Professor," published in 1946, are among the first in science fiction to introduce readers to the Moebius band, the Klein bottle, and the hypercube (tesseract)..
9. Diaz, Giovanna; O'Rourke, Joseph, Hypercube unfoldings that tile ${\displaystyle \mathbb {R} ^{3}}$ and ${\displaystyle \mathbb {R} ^{2}}$, 2015, Bibcode:2015arXiv151202086D, .
10. ^ Langerman, Stefan; Winslow, Andrew, Polycube unfoldings satisfying Conway's criterion (PDF), 19th Japan Conference on Discrete and Computational Geometry, Graphs, and Games (JCDCG^3 2016), 2016 [2022-08-12], （原始内容存档 (PDF)于2022-09-18）.
11. ^ Turney, Peter, Unfolding the tesseract, Journal of Recreational Mathematics, 1984, 17 (1): 1–16, MR 0765344