Mixed Polypent Compatibility

Introduction

Two or more polypents are compatible if there is a polypent that each of them can tile. Here I show some compatibilities for two polypents of different orders.

Nomenclature
Tripents and Tetrapents
Tripents and Pentapents
Tetrapents and Pentapents

Nomenclature

Tripents

Tetrapents

Pentapents

I use Erich Friedman's names for the pentapents.

Tripents and Tetrapents

Here are minimal figures for all tripent-tetrapent pairs.

3V 3C

4N 3:4 3:4

4L 3:4 3:4

4I 3:4 3:4

4J 3:4 3:4

4C 3:4 3:4

4T 3:4 6:8

4Y 3:4 3:4

	3V	3C
4N	3:4	3:4
4L	3:4	3:4
4I	3:4	3:4
4J	3:4	3:4
4C	3:4	3:4
4T	3:4	6:8
4Y	3:4	3:4

Tripents and Pentapents

Here are minimal figures for all tripent-pentapent pairs.

3V 3C

5A 6 10 3 5

5B 3 5 6 10

5C 12 20 3 5

5D 3 5 3 5

5E 3 5 6 10

5F 3 5 6 10

5G 3 5 3 5

5H 6 10 3 5

5I 6 10 3 5

5J 3 5 3 5

5K 6 10 3 5

5L 6 10 3 5

5M 3 5 3 5

5N 3 5 3 5

5P 3 5 3 5

5Q 3 5 6 10

5R 6 10 3 5

5S 3 5 3 5

5T 6 10 3 5

5U 3 5 3 5

5V 6 10 3 5

5W 3 5 6 10

5X 6 10 —

5Y 3 5 6 10

5Z 3 5 6 10

	3V	3C
5A	6 10	3 5
5B	3 5	6 10
5C	12 20	3 5
5D	3 5	3 5
5E	3 5	6 10
5F	3 5	6 10
5G	3 5	3 5
5H	6 10	3 5
5I	6 10	3 5
5J	3 5	3 5
5K	6 10	3 5
5L	6 10	3 5
5M	3 5	3 5
5N	3 5	3 5
5P	3 5	3 5
5Q	3 5	6 10
5R	6 10	3 5
5S	3 5	3 5
5T	6 10	3 5
5U	3 5	3 5
5V	6 10	3 5
5W	3 5	6 10
5X	6 10	—
5Y	3 5	6 10
5Z	3 5	6 10

3 Pentapents, 5 Tripents

6 Pentapents, 10 Tripents

12 Pentapents, 20 Tripents

Tetrapents and Pentapents

Here are minimal known figures for all compatible tetrapent-pentapent pairs.

4C 4I 4J 4L 4N 4T 4Y

5A 4:5 8:10 8:10 4:5 ? ? 4:5

5B 16:20 16:20 4:5 4:5 16:20 20:25 8:10

5C 4:5 8:10 4:5 8:10 ? 20:25 ?

5D 4:5 4:5 4:5 4:5 8:10 ? 8:10

5E 8:10 16:20 4:5 8:10 16:20 4:5 ?

5F 20:25 ? 8:10 4:5 ? 4:5 ?

5G 4:5 4:5 4:5 8:10 4:5 ? ?

5H 8:10 4:5 4:5 8:10 ? ? 4:5

5I 8:10 4:5 4:5 8:10 4:5 ? 8:10

5J 4:5 8:10 4:5 4:5 16:20 4:5 ?

5K 8:10 4:5 4:5 ? 4:5 ? 8:10

5L 4:5 4:5 4:5 4:5 ? ? 16:20

5M 20:25 ? 8:10 4:5 ? 8:10 ?

5N 4:5 4:5 4:5 8:10 4:5 ? 8:10

5P 8:10 4:5 4:5 4:5 8:10 ? 8:10

5Q 8:10 16:20 8:10 4:5 4:5 4:5 ?

5R 4:5 4:5 4:5 8:10 4:5 ? 8:10

5S 4:5 4:5 4:5 4:5 4:5 ? 8:10

5T 8:10 8:10 4:5 4:5 ? 4:5 ?

5U 16:20 4:5 4:5 20:25 ? ? ?

5V 8:10 16:20 4:5 4:5 ? ? ?

5W 4:5 4:5 16:20 ? 4:5 ? 8:10

5X ? ? ? ? ? 4:5 ?

5Y 4:5 4:5 8:10 4:5 8:10 ? 4:5

5Z 8:10 4:5 4:5 4:5 16:20 ? 8:10

	4C	4I	4J	4L	4N	4T	4Y
5A	4:5	8:10	8:10	4:5	?	?	4:5
5B	16:20	16:20	4:5	4:5	16:20	20:25	8:10
5C	4:5	8:10	4:5	8:10	?	20:25	?
5D	4:5	4:5	4:5	4:5	8:10	?	8:10
5E	8:10	16:20	4:5	8:10	16:20	4:5	?
5F	20:25	?	8:10	4:5	?	4:5	?
5G	4:5	4:5	4:5	8:10	4:5	?	?
5H	8:10	4:5	4:5	8:10	?	?	4:5
5I	8:10	4:5	4:5	8:10	4:5	?	8:10
5J	4:5	8:10	4:5	4:5	16:20	4:5	?
5K	8:10	4:5	4:5	?	4:5	?	8:10
5L	4:5	4:5	4:5	4:5	?	?	16:20
5M	20:25	?	8:10	4:5	?	8:10	?
5N	4:5	4:5	4:5	8:10	4:5	?	8:10
5P	8:10	4:5	4:5	4:5	8:10	?	8:10
5Q	8:10	16:20	8:10	4:5	4:5	4:5	?
5R	4:5	4:5	4:5	8:10	4:5	?	8:10
5S	4:5	4:5	4:5	4:5	4:5	?	8:10
5T	8:10	8:10	4:5	4:5	?	4:5	?
5U	16:20	4:5	4:5	20:25	?	?	?
5V	8:10	16:20	4:5	4:5	?	?	?
5W	4:5	4:5	16:20	?	4:5	?	8:10
5X	?	?	?	?	?	4:5	?
5Y	4:5	4:5	8:10	4:5	8:10	?	4:5
5Z	8:10	4:5	4:5	4:5	16:20	?	8:10

4 Pentapents, 5 Tetrapents

8 Pentapents, 10 Tetrapents

16 Pentapents, 20 Tetrapents

20 Pentapents, 25 Tetrapents

Last revised 2012-04-18.

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Col. George Sicherman [ HOME | MAIL ]