Shapes · 24-point badge
Combination shapes, 24-point
The centre tile fused with one to ten of the twenty-four tiles that touch it, by arc, point or cusp, wherever the added tiles join into one piece. 8,933 shapes behind 4,459 families, from 22,501 legal arrangements.
- Badge
- The 24-point badge
- Cards
- All 4,459 families on /shapes
- Books
- Book JBook ADBook AJ
- Patterns
- Patterns/patterns?shape=combination24-10-01
- Lock
- The lock
- Elsewhere
- 16-point combination shapesThe cousins
What changes from the 16-point badge
A New Shape separates the two variations as the badge without corners and the badge with corners, and leaves the second uncounted. The 16-point badge takes every tile that shares an arc with the centre tile. The 24-point badge takes every tile that touches it at all: the same sixteen, plus eight that meet it only at a point or a cusp. Arrangements are lettered A–X as in the badge specification. Circles (A–U) and diamonds (a–l) have letter sequences of their own; "arrangement C" and "circle C" are different things.
Everything else carries over unchanged. Two arrangements exclude each other when they share a circle or a diamond; the specification's exclusion table agrees with that rule for all twenty-four, including the B–X pair it corrects. A shape is a legal set whose added tiles form one piece, the centre tile not counted. A family is a shape with its turns and mirrors about the centre circle.
The count
| Tier | Legal | Shapes | Families | Unique |
|---|---|---|---|---|
| Tier 1 | 24 | 24 | 7 | 1 |
| Tier 2 | 234 | 72 | 25 | 0 |
| Tier 3 | 1,200 | 228 | 101 | 8 |
| Tier 4 | 3,521 | 687 | 331 | 1 |
| Tier 5 | 6,082 | 1,682 | 847 | 20 |
| Tier 6 | 6,216 | 2,632 | 1,320 | 8 |
| Tier 7 | 3,720 | 2,312 | 1,168 | 24 |
| Tier 8 | 1,264 | 1,056 | 534 | 12 |
| Tier 9 | 224 | 224 | 116 | 8 |
| Tier 10 | 16 | 16 | 10 | 4 |
| All | 22,501 | 8,933 | 4,459 | 86 |
The 22,501 legal arrangements agree line for line with the hand list in nuna-24pt-combinations.txt and with the lock's tier-10 count of 16. The same rules, applied to the 16-point badge, reproduce its reference exactly. Tier links open a card; the 24-point cards are drawn in the browser, so with JavaScript off they land on the drawer.
- Tier 1 · 7
- Tier 2 · 25
- Tier 3 · 101
- Tier 4 · 331
- Tier 5 · 847
- Tier 6 · 1,320
- Tier 7 · 1,168
- Tier 8 · 534
- Tier 9 · 116
- Tier 10 · 10
The largest
Ten families reach tier 10, eleven tiles in all; 4 of them are unique.
one of the ten largest
- 10·01ACFHJMORTV
- 10·02ACFHJMORTW
- 10·03ACFHJMPRTV
- 10·04ACFHJMPRTW
- 10·05ACFHKMORTV
- 10·06ACFHKMORTW
- 10·07ACFHKMPRTV
- 10·08ADFHJMORTV
- 10·09ADFHJMPRTV
- 10·10ADFHKMORTV
Open questions
- Connection rule. Every 24-point tile touches the centre, some only at a point. Keeping the 16-point rule (the centre does not count towards connection) keeps the two catalogues comparable. Counting contact with the centre as joining would change every number on this page.
- Numbering. Families are numbered by the same scheme as the 16-point reference (tier, then alphabetical by code). There is no 24-point technical reference to check that against.
- Marks. The build's MARK directive draws 16-point marks; whether it should take A–X codes as well is for the shell chat.
- Nuna life. The 24-point families have not been run.