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.

Here are minimal figures for all trihex-tetrahex pairs.

 3A3I3V
4I3:43:43:4
4J3:43:43:4
4O3:43:43:4
4Q3:43:43:4
4S3:43:43:4
4U6:86:83:4
4Y12:1612:163:4

Trihexes and Pentahexes.

Here are minimal figures for all trihex-pentahex pairs.

 3A3I3V
5A3:53:53:5
5C3:56:103:5
5D3:53:53:5
5E6:103:53:5
5F6:106:103:5
5H6:103:53:5
5I6:103:53:5
5J6:103:53:5
5K3:56:103:5
5L6:103:53:5
5N3:53:53:5
5P3:53:53:5
5Q3:56:103:5
5R3:53:53:5
5S6:103:53:5
5T6:106:103:5
5U6:106:103:5
5V6:103:53:5
5W6:103:53:5
5X3:56:103:5
5Y3:53:53:5
5Z6:103:53:5

Holeless Variants

Trihexes and Hexahexes.

Here are minimal known figures for all trihex-hexahex pairs.

Two Trihexes

Four Trihexes

More Trihexes

Holeless Variants

Tetrahexes and Pentahexes.

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

  4I 4J 4O 4Q 4S 4U 4Y
5A8:104:58:104:54:54:516:20
5C4:54:54:54:54:54:516:20
5D4:54:54:54:54:54:524:30
5E4:54:58:104:54:58:1016:20
5F4:54:54:54:54:54:58:10
5H4:54:58:104:54:54:54:5
5I4:54:54:54:54:58:10
5J4:54:54:54:54:54:512:15
5K4:54:54:54:54:54:54:5
5L4:54:54:54:54:54:516:20
5N8:104:54:54:54:54:58:10
5P4:54:54:54:54:54:58:10
5Q4:54:54:54:54:58:104:5
5R8:104:54:54:54:58:108:10
5S4:54:54:54:58:104:58:10
5T24:304:512:154:54:54:54:5
5U8:104:54:58:104:54:516:20
5V4:54:54:54:54:58:108:10
5W4:54:54:54:54:54:58:10
5X8:104:58:104:54:58:1032:40
5Y4:54:54:54:54:58:108:10
5Z4:54:54:54:54:54:58:10

Four Pentahexes, Five Tetrahexes

More Pentahexes and Tetrahexes

Holeless Variants

Tetrahexes and Hexahexes.

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

Two Hexahexes, Three Tetrahexes

Four Hexahexes, Six Tetrahexes

Six Hexahexes, Nine Tetrahexes

Eight Hexahexes, Twelve Tetrahexes

More Hexahexes and Tetrahexes

Holeless Variants

Pentahexes and Hexahexes.

There are too many pairs of pentahexes and hexahexes to show on this page. Here are the biggest minimal known ones.

60 Hexahexes, 72 Pentahexes

90 Hexahexes, 108 Pentahexes

Last revised 2011-09-16.


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Col. George Sicherman [ HOME | MAIL ]