5 × 10

9 × 20, 9 × 30, 9 × 45, 9 × 55

10 × 14, 10 × 16, 10 × 23, 10 × 27

11 × 20, 11 × 30, 11 × 35, 11 × 45

12 × 50, 12 × 55, 12 × 60, 12 × 65, 12 × 70,
12 × 75, 12 × 80, 12 × 85, 12 × 90, 12 × 95

13 × 20, 13 × 30, 13 × 35, 13 × 45

14 × 15

15 × 15, 15 × 16, 15 × 17, 15 × 19, 15 × 21,
15 × 22, 15 × 23

17 × 20, 17 × 25

18 × 25, 18 × 35

22 × 25

complete

smallest rectangle: 5 × 10

smallest odd rectangle: 15 × 15

The 5 × 10 rectangle was given by Klarner [6, Figure 2].
It has a tiling in which reflections are not used.
Marshall [8, Figures 5, 6, 7, 8] shows how to generalize this to get an
infinite family of rectifiable polyominoes.
In the meantime, many others [1, 2, 3, 4, 5, 7, 10] have looked for
more prime rectangles.
The complete set of primes was determined by Fogel, Goldenberg and Liu [4].
Also see [9, Example 5.2] for more analysis.
The smallest odd rectangle was found by Haselgrove [3].

Also see
Torsten
Sillke's Y pentomino page.

**References**

[1] James Bitner, Tiling 5n × 12 Rectangles with Y-pentominoes,
*Journal of Recreational Mathematics* **7** (1974),
pp. 276-278.

[2] C.J. Bouwkamp and D.A. Klarner, Packing a Box with Y-pentacubes,
*Journal of Recreational Mathematics* **3** (1970)
pp. 10-26.

[3] Andrejs Cibulis and Ilvars Mizniks, Tiling Rectangles with Pentominoes,
*Latvijas Universitātes Zinātniskie Raksti* **612**
(1998) pp. 57-61.

[4] Julian Fogel, Mark Goldenberg and Andy Liu,
Packing Rectangles with Y-Pentominoes,
*Mathematics and Informatics Quarterly* **11** (2001), no. 3,
pp. 133-137.

[5] Jenifer Haselgrove, Packing a Square with Y-pentominoes,
*Journal of Recreational Mathematics* **7** (1974), p. 229.

[6] David A. Klarner,
Some Results
Concerning Polyominoes,
*Fibonacci Quarterly* **3** (1965), no. 1, pp. 9-20.

[7] David A. Klarner, Letter to the Editor,
*Journal of Recreational Mathematics* **3** (1970), p. 258.

[8] William Rex Marshall,
Packing
Rectangles with Congruent Polyominoes,
*Journal of Combinatorial Theory, Series A* **77** (1997),
no. 2, pp. 181-192.

[9] Michael Reid,
Klarner Systems and Tiling
Boxes with Polyominoes,
*Journal of Combinatorial Theory, Series A* **111** (2005),
no. 1, pp. 89-105.

[10] Karl Scherer,
Some New Results on Y-pentominoes,
*Journal of Recreational Mathematics* **12** (1979-1980),
pp. 201-204.

Data for prime rectangles | Rectifiable polyominoes | Polyomino page | Home page | E-mail

Updated August 25, 2011.