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The Rubik’s Cluster Shell Model: A Novel Theory

已有 597 次阅读 2026-9-25 06:32 |个人分类:AEC 原子环境计算|系统分类:论文交流

10.5281/zenodo.22906505

Table 4 Wyckoff positions in space group No. 221, the corresponding cubies

of the Rubik’s cube, and the degeneracies (Deg.) of their generalized orbits

Some Wyckoff positions in No. 221 do not have corresponding cubies,

but they can be matched with virtual cubies. It is worth noting that

the degeneracy of the generalized orbits multiplied by the coordination number

of the shell is exactly equal to the order of the

Multiplicity & Wyckoff letter	Cubies in the Cube/ Positions in No. 221	3×3×3 〈〉, CN	5×5×5 〈〉, CN	7×7×7 〈〉, CN	Deg.
1 a	Corner cubies/ (0, 0, 0)	〈111〉, 8	〈222〉, 8	〈333〉, 8	6
1 b	Cube center/ (1/2, 1/2, 1/2)	〈000〉, 1	〈000〉, 1	〈000〉, 1	48
3 c	Center cubies/ (0, 1/2, 1/2)	〈100〉, 6	〈200〉, 6	〈300〉, 6	8
3 d	Edge midpoint cubies/ (1/2, 0, 0)	〈110〉, 12	〈220〉, 12	〈330〉, 12	4
6 e	Edge cubies/		〈221〉, 24	〈331〉, 24 〈332〉, 24	2
6 f	(x,1/2,1/2)				8
8 g					6
12 h	Face cross cubies/ (x,1/2,0)		〈210〉, 24	〈310〉, 24 〈320〉, 24	2
12 i	Face diagonal cubies/ (0, y, y)		〈211〉, 24	〈311〉, 24 〈322〉, 24	2
12 j	(1/2, y, y)				4
24 k	Face general cubies/ (0, y, z)			〈321〉, 48	1
24 l	(1/2, y, z)				2
24 m					2
48 n					1