#7B: 2-1-1-1-2-0
Panels can contain as many triangles as desired. The minimum is 1, but larger numbers will often be preferred for convenience, in particular to reduce setup and teardown time.
All the convex panels through size 15 are illustrated below; some form mirror-image pairs. The dotted lines emphasize how each is a polyiamond based on a unit triangle. Here is an example from the tables below:
#7B: 2-1-1-1-2-0 |
The six-digit sequence represents the lengths of the edges, starting at the top, and moving clockwise. A length of zero results in an acute angle. Canonical is to start numbering with the longest edge; in case of ties, the second number prevails.
For instance, panel #7B above could be correctly designated according to any of these six rotations:
The canonical form would have to be either 2-0-2-1-1-1 or 2-1-1-1-2-0, as they each lead with the largest number. The latter of these has 1 in the second position while the former has 0, so 2-1-1-1-2-0 becomes the canonical form. The panel will, for catalog purposes, be drawn with one edge of length 2 at the top, and a 1 (not 0) at the top right.
Assume the edges are letterered clockwise from the top a-b-c-d-e-f. A panel some of whose edges are equal in the pattern ...
A formula for the quantity of triangles within the panel is (a + b + c)2 − a2 − c2 − e2.
For a treatment of a related subject, see equiangular hexagons.
Panels of sizes 1, 2, 3, and 5 are unique, so their designator does not require a letter:
 #1: 1-0-1-0-1-0 |  #2: 1-1-0-1-1-0 |  #3: 2-0-1-1-1-0 |  #5: 3-0-1-2-1-0 |
Other sizes have letters assigned in increasing order, based on descending lexicographical order of the six numbers. Mirror-image pairs are rendered here in a color other than yellow, and might not have consecutive letters.
 #4A: 2-1-0-2-1-0  #4C: 2-0-1-2-0-1 |  #4B: 2-0-2-0-2-0 |
 #6A: 3-1-0-3-1-0  #6B: 3-0-1-3-0-1 |  #6C: 1-1-1-1-1-1 |
 #7A: 4-0-1-3-1-0 | #7B: 2-1-1-1-2-0 |
 #8A: 4-1-0-4-1-0  #8B: 4-0-1-4-0-1 |  #8C: 3-0-2-1-2-0 |  #8D: 2-2-0-2-2-0 |
 #9A: 5-0-1-4-1-0 |  #9B: 3-0-3-0-3-0 |
 #10A: 5-1-0-5-1-0  #10B: 5-0-1-5-0-1 |  #10C: 2-1-1-2-1-1 |
 #11A: 6-0-1-5-1-0 |  #11B: 3-1-1-2-2-0  #11C: 3-0-2-2-1-1 |
 #12A: 6-1-0-6-1-0  #12B: 6-0-1-6-0-1 |  #12C: 4-0-2-2-2-0 |  #12D: 3-2-0-3-2-0  #12E: 3-0-2-3-0-2 |
 #13A: 7-0-1-6-1-0 |  #13B: 2-1-2-1-2-1 |
 #14A: 7-1-0-7-1-0  #14B: 7-0-1-7-0-1 | |
 #14C: 3-1-2-1-3-0 |  #14D: 3-1-1-3-1-1 |
 #15A: 8-0-1-7-1-0 | |
 #15C: 4-0-3-1-3-0 |  #15B: 4-1-1-3-2-0  #15D: 4-0-2-3-1-1 |
The table below lists all convex panels through size 24 including everything above. Also listed are the panels' periods, and the number of axes of reflective symmetry. There is no simple formula to determine how many panels of each size there will be. The sequence of sizes was not found in OEIS.
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