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You may also see list of all polyomino sets for which data is available here.
Area: 9.
Size: 3x5.
Is rectangular: no.
Is convex: yes.
Holes: 0.
Order: 4.
Square order: 4.
Prime rectangles: ≥ 22.
Smallest rectangle and smallest square (6x6):
Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).
Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).
Purple number - prime rectangle (unknown if weakly or strongly prime).
Red number - composite rectangle (which can be divided into two rectangles tileable by this set).
Gray number - it is unknown whether rectangle is prime or composite.
Question mark (?) - solution count is unknown.
Click on underlined numbers to view picture with one solution.
$N(w; h)$ - number of ways to tile $w\times h$ rectangle (including symmetric solutions)
$T(w; h) = \begin{cases} 1, & N(w; h) \geq 1 \\ 0, & \text{else} \end{cases}$ - tileability function, $1$ if tiles rectangle, $0$ otherwise
$A(w; h) = \left(N(w; h)\right)^{\frac{1}{wh}}$ - average number of ways to tile cell in $w\times h$ rectangle (including symmetric solutions)
$G(T; x; y) = \sum_{w=1}^{\infty}\sum _{h=1}^{\infty}T(w; h)x^wy^h$ - bivariate generating function of $T(w; h)$
$G(A; x; y) = \sum_{w=1}^{\infty}\sum _{h=1}^{\infty}A(w; h)x^wy^h$ - bivariate generating function of $A(w; h)$
$N(6; n) = 3 \times N(6; n - 6), \qquad n \geq 7 \tag{1}$
$N(12; n) = 29 \times N(12; n - 6) - 272 \times N(12; n - 12) + 988 \times N(12; n - 18) - 1515 \times N(12; n - 24) + 819 \times N(12; n - 30), \qquad n \geq 31 \tag{2}$
$G(N(6); x) = \frac{1 - x^6}{1 - 3x^6} \tag{2}$
