A correction: the negative result from the last post does not apply to p6 or p10, because my search methodology was unintentionally non-exhaustive for periods with multiple distinct prime factors.

Here are some billiard tables. Most are probably known but I can't check at the moment, but a few might potentially be new:

(Medium p5, might be new)

Code: Select all

```
x = 18, y = 14, rule = B3/S23
4bo$2b3o$bo10b2o$bo2b3o4bo2bo$2obo3bo3bob2o$3bobo2bob2o$3bobo6b5o$4b2o
b4o6bo$6bo5b5o$6bob3o$7b2o2b2o2b2o$11bo4bo$12bo2bo$11b2o2b2o!
```

(Tiny p7, probably known)

Code: Select all

```
x = 9, y = 11, rule = B3/S23
4b2o$2o2bo2bo$obobob2o$2bobo$4bob2o$7bo$bo2bobo$b4ob2o$5bo2bo$3bo3b2o
$3b2o!
```

(Burloaferimeter phase-shifting a p3 at p7, probably but not necessarily known)

Code: Select all

```
x = 13, y = 11, rule = B3/S23
4b2o$2obob3o$ob2o4bo$5b3obo$b3o5bo$bo3b2o2bob2o$2b3o4bob2o$5b4o$4bo$4b
obo$5b2o!
```

(Small p8, probably but not necessarily known)

Code: Select all

```
x = 14, y = 10, rule = B3/S23
6bo$6b3o$9bo$4b3ob2o$3bo2bobo$3bo4bo$2obo4bob2obo$bobobobo2bob2o$bobo
bo4bo$2b2ob2o2b2o!
```

(Larger p8, might be new)

Code: Select all

```
x = 19, y = 14, rule = B3/S23
5b2o3bo$6bo2bobo$5bo3b2o$4bob3o$bo2bo4b4o$obobob3o4bo$bo2bo4b4obo$4bo
b4o4bo2bo$5bo4bobobobobo$6b4o4bo2bo$10b3obo$8b2o3bo$7bobo2bo$8bo3b2o!
```

(Large but possibly reducible p8, component probably known)

Code: Select all

```
x = 14, y = 16, rule = B3/S23
5b2o$5bo$6bo$3b3obo$3bo2bobo$o3bobobo$4obo2bob2o$8bobobo$2bob3obobo2b
o$2b2o7b2o$5b3obobo$2b3o3b2obo$2bo2b2o3bo$4bo2b3o$5bobo$6bo!
```

EDITs:

(P5 phase-shifting a p3 at p10, might be new)

Code: Select all

```
x = 15, y = 15, rule = B3/S23
5b2o$6bo$4bo2b2o$2obob2o2bo$ob2o3b2obo$4b3o2bo$b4o2b2o$bo3b3o5b2o$2b3o
3bo2bo2bo$5b3obob3o$2b2o4b2o$3bob2o3b2o$3bobo4bobo$2b2o2bo4bo$5b2o!
```

(Drifter-y p10, probably known)

Code: Select all

```
x = 16, y = 13, rule = B3/S23
2bo$bobo$bobo$2ob2o5b2o$2bo3b2o3bo$2bob2o4bo$3bo6bobob2o$4b3obobob2ob
o$7b2obo$4b2o4bo$4bo5b2o$5bo$4b2o!
```