|
|
A293060
|
|
Triangle read by rows (n >= 0, 0 <= k <= n): T(n,k) = number of k-dimensional subperiodic groups in n-dimensional space, not counting enantiomorphs.
|
|
4
|
|
|
1, 2, 2, 10, 7, 17, 32, 67, 80, 219, 227, 343, 1076, 1594, 4783, 955
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
T(n,0) count n-dimensional crystallographic point groups (i.e., left border is A004028), T(n,n) count n-dimensional space groups (i.e., right border is A004029). The name "subperiodic groups" is usually related to the case 0 < k < n only, i.e., symmetry groups of n-dimensional objects including k independent translations which are subgroups of some n-dimensional space groups.
The Bohm symbols for these groups are G_{n,k}, except for the case k=n, when it is G_n.
Some groups have their own names:
T(2,1): frieze groups
T(2,2): wallpaper groups
T(3,1): rod groups
T(3,2): layer groups
See [Palistrant, 2012, p. 476] for row 4.
|
|
LINKS
|
W. Plesken and T. Schulz, CARAT Homepage [Cached copy in pdf format (without subsidiary pages), with permission]
|
|
EXAMPLE
|
The triangle begins:
1;
2, 2;
10, 7, 17;
32, 67, 80, 219;
227, 343, 1076, 1594, 4783;
955, ...
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|