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Area: 20.
Perimeter: 18.
Size: 3x10.
Is rectangular: no.
Is convex: yes.
Holes: 0.
Order: 12.
Square order: 20.
Prime rectangles: ≥ 3.
Smallest rectangle (12x20):
Smallest square (20x20):
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 $A(w; h)$
$N(12; n) = 2 \times N(12; n - 20), \qquad n \geq 21 \tag{1}$
$G(N(12); x) = \frac{1}{1 - 2x^{20}} \tag{2}$
$N(16; n) = 2 \times N(16; n - 20), \qquad n \geq 21 \tag{3}$
$G(N(16); x) = \frac{1}{1 - 2x^{20}} \tag{4}$
$G(N(20); x) = \frac{1 - x^4}{1 - x^4 - 2x^{12}} \tag{5}$
$G(N(24); x) = \frac{1 - 2x^{20}}{1 - 8x^{20} + 8x^{40}} \tag{6}$
$G(N(28); x) = \frac{1 - 3x^{20}}{1 - 13x^{20} + 24x^{40}} \tag{7}$
$G(N(32); x) = \frac{1 - 24x^{20} - 8x^{40} + 256x^{60}}{1 - 38x^{20} - 100x^{40} + 416x^{60} + 1024x^{80}} \tag{8}$
