Mixed Polyhex Compatibility

Introduction.

Two or more polyhexes are compatible if there is a polyhex that each of them can tile. Here I show some compatibilities for two polyhexes of different orders. Some of them were found by Andris Cibulis.

For pentahex-pentahex compatibility, see Pentahex Compatibility.

Trihexes and Tetrahexes
Trihexes and Pentahexes
Tetrahexes and Pentahexes

Trihexes and Tetrahexes.

Here are minimal figures for all trihex-tetrahex pairs.

3:4 3:4 3:4

3:4 3:4 3:4

3:4 3:4 3:4

3:4 3:4 3:4

3:4 3:4 3:4

6:8 6:8 3:4

12:16 12:16 3:4


3:4	3:4	3:4
3:4	3:4	3:4
3:4	3:4	3:4
3:4	3:4	3:4
3:4	3:4	3:4
6:8	6:8	3:4
12:16	12:16	3:4

Trihexes and Pentahexes.

Here are minimal figures for all trihex-pentahex pairs.

3:5 3:5 3:5

3:5 6:10 3:5

3:5 3:5 3:5

6:10 3:5 3:5

6:10 6:10 3:5

6:10 3:5 3:5

6:10 3:5 3:5

6:10 3:5 3:5

3:5 6:10 3:5

6:10 3:5 3:5

3:5 3:5 3:5

3:5 3:5 3:5

3:5 6:10 3:5

3:5 3:5 3:5

6:10 3:5 3:5

6:10 6:10 3:5

6:10 6:10 3:5

6:10 3:5 3:5

6:10 3:5 3:5

3:5 6:10 3:5

3:5 3:5 3:5

6:10 3:5 3:5


3:5	3:5	3:5
3:5	6:10	3:5
3:5	3:5	3:5
6:10	3:5	3:5
6:10	6:10	3:5
6:10	3:5	3:5
6:10	3:5	3:5
6:10	3:5	3:5
3:5	6:10	3:5
6:10	3:5	3:5
3:5	3:5	3:5
3:5	3:5	3:5
3:5	6:10	3:5
3:5	3:5	3:5
6:10	3:5	3:5
6:10	6:10	3:5
6:10	6:10	3:5
6:10	3:5	3:5
6:10	3:5	3:5
3:5	6:10	3:5
3:5	3:5	3:5
6:10	3:5	3:5

Tetrahexes and Pentahexes.

Here are minimal known figures for all compatible tetrahex-pentahex pairs.

8:10 4:5 8:10 4:5 4:5 4:5 16:20

4:5 4:5 4:5 4:5 4:5 4:5 16:20

4:5 4:5 4:5 4:5 4:5 4:5 24:30

4:5 4:5 8:10 4:5 4:5 8:10 16:20

4:5 4:5 4:5 4:5 4:5 4:5 8:10

4:5 4:5 8:10 4:5 4:5 4:5 4:5

4:5 4:5 4:5 4:5 4:5 8:10 —

4:5 4:5 4:5 4:5 4:5 4:5 12:15

4:5 4:5 4:5 4:5 4:5 4:5 4:5

4:5 4:5 4:5 4:5 4:5 4:5 16:20

8:10 4:5 4:5 4:5 4:5 4:5 8:10

4:5 4:5 4:5 4:5 4:5 4:5 8:10

4:5 4:5 4:5 4:5 4:5 8:10 4:5

8:10 4:5 4:5 4:5 4:5 8:10 8:10

4:5 4:5 4:5 4:5 8:10 4:5 8:10

24:30 4:5 12:15 4:5 4:5 4:5 4:5

8:10 4:5 4:5 8:10 4:5 4:5 16:20

4:5 4:5 4:5 4:5 4:5 8:10 8:10

4:5 4:5 4:5 4:5 4:5 4:5 8:10

8:10 4:5 8:10 4:5 4:5 8:10 32:40

4:5 4:5 4:5 4:5 4:5 8:10 8:10

4:5 4:5 4:5 4:5 4:5 4:5 8:10


8:10	4:5	8:10	4:5	4:5	4:5	16:20
4:5	4:5	4:5	4:5	4:5	4:5	16:20
4:5	4:5	4:5	4:5	4:5	4:5	24:30
4:5	4:5	8:10	4:5	4:5	8:10	16:20
4:5	4:5	4:5	4:5	4:5	4:5	8:10
4:5	4:5	8:10	4:5	4:5	4:5	4:5
4:5	4:5	4:5	4:5	4:5	8:10	—
4:5	4:5	4:5	4:5	4:5	4:5	12:15
4:5	4:5	4:5	4:5	4:5	4:5	4:5
4:5	4:5	4:5	4:5	4:5	4:5	16:20
8:10	4:5	4:5	4:5	4:5	4:5	8:10
4:5	4:5	4:5	4:5	4:5	4:5	8:10
4:5	4:5	4:5	4:5	4:5	8:10	4:5
8:10	4:5	4:5	4:5	4:5	8:10	8:10
4:5	4:5	4:5	4:5	8:10	4:5	8:10
24:30	4:5	12:15	4:5	4:5	4:5	4:5
8:10	4:5	4:5	8:10	4:5	4:5	16:20
4:5	4:5	4:5	4:5	4:5	8:10	8:10
4:5	4:5	4:5	4:5	4:5	4:5	8:10
8:10	4:5	8:10	4:5	4:5	8:10	32:40
4:5	4:5	4:5	4:5	4:5	8:10	8:10
4:5	4:5	4:5	4:5	4:5	4:5	8:10

Four Pentahexes, Five Tetrahexes

More Pentahexes and Tetrahexes

Last revised 2008-07-23.

Back to Polyform Curiosities.

Col. George Sicherman [ HOME | MAIL ]