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    Quadrilateral Laminae

    Named laminae

    diamond | golden rectangle | golden rhombus | half rectangle | half square | isosceles trapezoid | kite | lozenge | monokite | parallelogram | quarter rectangle | quarter square | rectangle | regular diamond | rhombus | right trapezoid | square | trapezoid | inverted isosceles trapezoid (total: 19)

    Definitions

    Definitions Diamond

    Definitions Golden rectangle

    Definitions Golden rhombus

    Defining inequalities

    abs(x)/a + abs(y)/b<=1

    -a/2<=x<=a/2 and -(a Ï•)/2<=y<=(a Ï•)/2

    2 (1 + sqrt(5)) a + sqrt(2 (5 + sqrt(5))) (2 x + sqrt(5) y + y)>=0 and 2 (1 + sqrt(5)) a + sqrt(2 (5 + sqrt(5))) (-2 x + sqrt(5) y + y)>=0 and 2 sqrt(5 (5 + sqrt(5))) a>=5 sqrt(2) (2 x + sqrt(5) y + y) and 2 (1 + sqrt(5)) a>=sqrt(2 (5 + sqrt(5))) (-2 x + sqrt(5) y + y)

    -a/2<=x<=a/2 and 0<=y<=b/2

    -a/2<=x<=a/2 and 0<=y<=a/2

    0<=y<=h and a y + b h>=b y + 2 h x and a y + b h>=b y - 2 h x

    h (sqrt(a^2 - h^2) + x) + y sqrt(a^2 - h^2)>=0 and sqrt((b - h) (b + h)) (h + y)>=h x and h sqrt(b^2 - h^2)>=y sqrt(b^2 - h^2) + h x and h (sqrt(a^2 - h^2) + x)>=y sqrt(a^2 - h^2)

    y>=0 and a + y>=x and sqrt(2) a>=2 y and x>=y

    sqrt(3) y>=3 x and 2 sqrt(3) a>=x + sqrt(3) y and 2 sqrt(3) a + x>=sqrt(3) y and 3 x + sqrt(3) y>=0

    y>=0 and b sin(A) + y cos(A)>=x sin(A) and a sin(A)>=y and x sin(A)>=y cos(A)

    Alternate names

    isosceles trapezium

    equiangular rectangle

    diamond | equilateral parallelogram | rhomb

    right trapezium

    trapezium

    inverted isosceles trapezium

    Lamina properties

    diamond | (-a, 0) | (0, -b) | (a, 0) | (0, b) golden rectangle | (a/2, -(ϕ a)/2) | (a/2, (ϕ a)/2) | (-a/2, (ϕ a)/2) | (-a/2, -(ϕ a)/2) golden rhombus | (-a/(2 sqrt(5/8 - sqrt(5)/8)), 0) | (0, -a/(2 sqrt(5/8 + sqrt(5)/8))) | (a/(2 sqrt(5/8 - sqrt(5)/8)), 0) | (0, a/(2 sqrt(5/8 + sqrt(5)/8))) half rectangle | (-a/2, 0) | (a/2, 0) | (a/2, b/2) | (-a/2, b/2) half square | (-a/2, 0) | (a/2, 0) | (a/2, a/2) | (-a/2, a/2) isosceles trapezoid | (-b/2, 0) | (b/2, 0) | (a/2, h) | (-a/2, h) kite | (-sqrt(a^2 - h^2), 0) | (0, -h) | (sqrt(b^2 - h^2), 0) | (0, h) lozenge | (0, 0) | (a, 0) | ((1 + 1/sqrt(2)) a, a/sqrt(2)) | (a/sqrt(2), a/sqrt(2)) monokite | (0, 0) | ((sqrt(3) a)/2, (3 a)/2) | (0, 2 a) | (-(sqrt(3) a)/2, (3 a)/2) parallelogram | (0, 0) | (b, 0) | (cos(A) a + b, sin(A) a) | (cos(A) a, sin(A) a) quarter rectangle | (0, 0) | (a/2, 0) | (a/2, b/2) | (0, b/2) quarter square | (0, 0) | (a/2, 0) | (a/2, a/2) | (0, a/2) rectangle | (-a/2, -b/2) | (a/2, -b/2) | (a/2, b/2) | (-a/2, b/2) regular diamond | (-a, 0) | (0, -a) | (a, 0) | (0, a) rhombus | (-cos(θ) a, 0) | (0, -sin(θ) a) | (cos(θ) a, 0) | (0, sin(θ) a) right trapezoid | (0, 0) | (a, 0) | (a, h_2) | (0, h_1) square | (-a/2, -a/2) | (a/2, -a/2) | (a/2, a/2) | (-a/2, a/2) trapezoid | (0, 0) | (b, 0) | ((a^2 - b^2 - c^2 + d^2)/(2 (a - b)), sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (-a + b))) | (-(a^2 - 2 a b + b^2 + c^2 - d^2)/(2 (a - b)), sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (-a + b))) inverted isosceles trapezoid | (-b/2, 0) | (b/2, 0) | (a/2, sqrt(-1/4 (-a + b)^2 + c^2)) | (-a/2, sqrt(-1/4 (-a + b)^2 + c^2))

    diamond | 4 golden rectangle | 4 golden rhombus | 4 half rectangle | 4 half square | 4 isosceles trapezoid | 4 kite | 4 lozenge | 4 monokite | 4 parallelogram | 4 quarter rectangle | 4 quarter square | 4 rectangle | 4 regular diamond | 4 rhombus | 4 right trapezoid | 4 square | 4 trapezoid | 4 inverted isosceles trapezoid | 4

    diamond | a>0 and b>0 golden rectangle | a>0 golden rhombus | a>0 half rectangle | a>0 and b>0 half square | a>0 isosceles trapezoid | 0<a<b and h>0 kite | 0<h<a and 0<h<b lozenge | a>0 monokite | a>0 parallelogram | a>0 and b>0 and 0<A<π quarter rectangle | a>0 and b>0 quarter square | a>0 rectangle | a>0 and b>0 regular diamond | a>0 rhombus | a>0 and 0<θ<π/2 right trapezoid | a>0 and h_1>0 and h_2>0 square | a>0 trapezoid | a>0 and b>0 and c>0 and d>0 and (a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)>0 inverted isosceles trapezoid | 0<b<a and c>(a - b)/2

    diamond | 2 a | 2 b golden rectangle | a sqrt(ϕ^2 + 1) | a sqrt(ϕ^2 + 1) golden rhombus | a/sqrt(5/8 - sqrt(5)/8) | a/sqrt(5/8 + sqrt(5)/8) isosceles trapezoid | 1/2 sqrt((a + b)^2 + 4 h^2) | 1/2 sqrt((a + b)^2 + 4 h^2) kite | sqrt(a^2 - h^2) + sqrt(b^2 - h^2) | 2 h lozenge | sqrt(2 + sqrt(2)) a | sqrt(2 - sqrt(2)) a monokite | 2 a | sqrt(3) a parallelogram | sqrt(a^2 - 2 a b cos(A) + b^2) | sqrt(a^2 + 2 a b cos(A) + b^2) rectangle | sqrt(a^2 + b^2) | sqrt(a^2 + b^2) regular diamond | 2 a | 2 a rhombus | 2 a cos(θ) | 2 a sin(θ) right trapezoid | sqrt(a^2 + h_1^2) | sqrt(a^2 + h_2^2) square | sqrt(2) a | sqrt(2) a trapezoid | sqrt((a^2 (-b) + a b^2 - a c^2 + b d^2)/(b - a)) | sqrt((a^2 (-b) + a b^2 - a d^2 + b c^2)/(b - a)) inverted isosceles trapezoid | sqrt(a b + c^2) | sqrt(a b + c^2)

    square | r = a/2

    square | h = 1/2 (sqrt(2) - 1) a

    golden rectangle | a Ï• half rectangle | b/2 half square | a/2 isosceles trapezoid | h monokite | 2 a parallelogram | a sin(A) quarter rectangle | b/2 quarter square | a/2 rectangle | b square | a trapezoid | sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))/(2 (b - a)) inverted isosceles trapezoid | sqrt(c^2 - 1/4 (b - a)^2)

    diamond | A = 2 a b golden rectangle | A = a^2 ϕ golden rhombus | A = (2 a^2)/sqrt(5) half rectangle | A = (a b)/2 half square | A = a^2/2 isosceles trapezoid | A = 1/2 h (a + b) kite | A = h (sqrt(a^2 - h^2) + sqrt(b^2 - h^2)) lozenge | A = a^2/sqrt(2) monokite | A = sqrt(3) a^2 parallelogram | A = a b sin(A) quarter rectangle | A = (a b)/4 quarter square | A = a^2/4 rectangle | A = a b regular diamond | A = 2 a^2 rhombus | A = a^2 sin(2 θ) right trapezoid | A = 1/2 a (h_1 + h_2) square | A = a^2 trapezoid | A = ((a + b) sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)))/(4 (b - a)) inverted isosceles trapezoid | A = 1/4 (a + b) sqrt(4 c^2 - (b - a)^2)

    diamond | x^_ = (0, 0) golden rectangle | x^_ = (0, 0) golden rhombus | x^_ = (0, 0) half rectangle | x^_ = (0, b/4) half square | x^_ = (0, a/4) isosceles trapezoid | x^_ = (0, ((2 a + b) h)/(3 (a + b))) kite | x^_ = (1/3 (-sqrt(a^2 - h^2) + sqrt(b^2 - h^2)), 0) lozenge | x^_ = (1/4 (2 + sqrt(2)) a, a/(2 sqrt(2))) monokite | x^_ = (0, (7 a)/6) parallelogram | x^_ = (1/2 (cos(A) a + b), 1/2 sin(A) a) quarter rectangle | x^_ = (a/4, b/4) quarter square | x^_ = (a/4, a/4) rectangle | x^_ = (0, 0) regular diamond | x^_ = (0, 0) rhombus | x^_ = (0, 0) right trapezoid | x^_ = ((a (h_1 + 2 h_2))/(3 (h_1 + h_2)), 1/3 (h_2 + h_1^2/(h_1 + h_2))) square | x^_ = (0, 0) trapezoid | x^_ = (b/2 + ((2 a + b) (c^2 - d^2))/(6 (-a^2 + b^2)), ((2 a + b) sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)))/(6 (-a^2 + b^2))) inverted isosceles trapezoid | x^_ = (0, ((2 a + b) sqrt(-(-a + b)^2 + 4 c^2))/(6 (a + b)))

    Mechanical properties

    diamond | J_x invisible comma x = (a b^3)/3 golden rectangle | J_x invisible comma x = (a^4 ϕ^3)/12 golden rhombus | J_x invisible comma x = (a^4 ϕ)/(3 (ϕ^2 + 1)^2) half rectangle | J_x invisible comma x = (a b^3)/24 half square | J_x invisible comma x = a^4/24 isosceles trapezoid | J_x invisible comma x = 1/12 h^3 (3 a + b) kite | J_x invisible comma x = 1/6 h^3 (sqrt(a^2 - h^2) + sqrt(b^2 - h^2)) lozenge | J_x invisible comma x = a^4/(6 sqrt(2)) monokite | J_x invisible comma x = (37 a^4)/(8 sqrt(3)) parallelogram | J_x invisible comma x = 1/3 a^3 b sin^3(A) quarter rectangle | J_x invisible comma x = (a b^3)/48 quarter square | J_x invisible comma x = a^4/48 rectangle | J_x invisible comma x = (a b^3)/12 regular diamond | J_x invisible comma x = a^4/3 rhombus | J_x invisible comma x = 1/3 a^4 sin^3(θ) cos(θ) right trapezoid | J_x invisible comma x = 1/12 a (h_1 + h_2) (h_1^2 + h_2^2) square | J_x invisible comma x = a^4/12 trapezoid | J_x invisible comma x = -((3 a + b) ((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d))^(3/2))/(96 (a - b)^3) inverted isosceles trapezoid | J_x invisible comma x = 1/96 (3 a + b) (4 c^2 - (b - a)^2)^(3/2)

    diamond | J_y invisible comma y = (a^3 b)/3 golden rectangle | J_y invisible comma y = (a^4 ϕ)/12 golden rhombus | J_y invisible comma y = (a^4 ϕ^3)/(3 (ϕ^2 + 1)^2) half rectangle | J_y invisible comma y = (a^3 b)/24 half square | J_y invisible comma y = a^4/24 isosceles trapezoid | J_y invisible comma y = 1/48 h (a + b) (a^2 + b^2) kite | J_y invisible comma y = 1/6 h ((a^2 - h^2)^(3/2) + (b^2 - h^2)^(3/2)) lozenge | J_y invisible comma y = 1/4 (1 + sqrt(2)) a^4 monokite | J_y invisible comma y = (sqrt(3) a^4)/8 parallelogram | J_y invisible comma y = 1/6 a b sin(A) (a^2 cos(2 A) + a^2 + 3 a b cos(A) + 2 b^2) quarter rectangle | J_y invisible comma y = (a^3 b)/48 quarter square | J_y invisible comma y = a^4/48 rectangle | J_y invisible comma y = (a^3 b)/12 regular diamond | J_y invisible comma y = a^4/3 rhombus | J_y invisible comma y = 1/3 a^4 sin(θ) cos^3(θ) right trapezoid | J_y invisible comma y = 1/12 a^3 (h_1 + 3 h_2) square | J_y invisible comma y = a^4/12 trapezoid | J_y invisible comma y = -(sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) (a^5 - a^4 b + 6 a^3 b^2 - 6 a^2 b^3 - 8 a^2 b c^2 + 8 a^2 b d^2 - 7 a b^4 + 4 a b^2 c^2 - 4 a b^2 d^2 + 3 a c^4 - 6 a c^2 d^2 + 3 a d^4 + 7 b^5 + 4 b^3 c^2 - 4 b^3 d^2 + b c^4 - 2 b c^2 d^2 + b d^4))/(96 (a - b)^3) inverted isosceles trapezoid | J_y invisible comma y = 1/96 (a + b) (a^2 + b^2) sqrt(4 c^2 - (b - a)^2)

    diamond | J_zz = 1/3 a b (a^2 + b^2) golden rectangle | J_zz = 1/12 a^4 ϕ (ϕ^2 + 1) golden rhombus | J_zz = (a^4 ϕ)/(3 (ϕ^2 + 1)) half rectangle | J_zz = 1/24 a b (a^2 + b^2) half square | J_zz = a^4/12 isosceles trapezoid | J_zz = 1/48 h ((a + b) (a^2 + b^2) + 4 h^2 (3 a + b)) kite | J_zz = 1/6 h (a^2 sqrt(a^2 - h^2) + b^2 sqrt(b^2 - h^2)) lozenge | J_zz = 1/12 (3 + 4 sqrt(2)) a^4 monokite | J_zz = (5 a^4)/sqrt(3) parallelogram | J_zz = 1/6 a b sin(A) (2 (a^2 + b^2) + 3 a b cos(A)) quarter rectangle | J_zz = 1/48 a b (a^2 + b^2) quarter square | J_zz = a^4/24 rectangle | J_zz = 1/12 a b (a^2 + b^2) regular diamond | J_zz = (2 a^4)/3 rhombus | J_zz = 1/6 a^4 sin(2 θ) right trapezoid | J_zz = 1/12 a (a^2 (h_1 + 3 h_2) + (h_1 + h_2) (h_1^2 + h_2^2)) square | J_zz = a^4/6 trapezoid | J_zz = (sqrt((a - b + c - d) (a - b - c + d) (a - b + c + d) (-a + b + c + d)) (a^4 - 4 a^3 b - 3 a^2 (c^2 + d^2) + a b (6 c^2 - 2 d^2) + b^2 (3 b^2 + 3 c^2 - d^2)))/(48 (a - b)^2) inverted isosceles trapezoid | J_zz = 1/96 (a + b) (a^2 + b^2) sqrt(4 c^2 - (a - b)^2) + 1/96 (3 a + b) (4 c^2 - (a - b)^2)^(3/2)

    diamond | J_x invisible comma y = 0 golden rectangle | J_x invisible comma y = 0 golden rhombus | J_x invisible comma y = 0 half rectangle | J_x invisible comma y = 0 half square | J_x invisible comma y = 0 isosceles trapezoid | J_x invisible comma y = 0 kite | J_x invisible comma y = 0 lozenge | J_x invisible comma y = -1/24 (3 + 2 sqrt(2)) a^4 monokite | J_x invisible comma y = 0 parallelogram | J_x invisible comma y = -1/12 a^2 b sin^2(A) (4 a cos(A) + 3 b) quarter rectangle | J_x invisible comma y = -1/64 a^2 b^2 quarter square | J_x invisible comma y = -a^4/64 rectangle | J_x invisible comma y = 0 regular diamond | J_x invisible comma y = 0 rhombus | J_x invisible comma y = 0 right trapezoid | J_x invisible comma y = -1/24 a^2 (h_1^2 + 2 h_2 h_1 + 3 h_2^2) square | J_x invisible comma y = 0 trapezoid | J_x invisible comma y = ((a - b - c - d) (a - b + c - d) (a - b - c + d) (a - b + c + d) (2 b (2 a^2 + c^2) - (a + b) (2 b^2 + 3 c^2) + d^2 (3 a + b)))/(96 (a - b)^3) inverted isosceles trapezoid | J_x invisible comma y = 0

    diamond | r_x = b/sqrt(6) r_y = a/sqrt(6) golden rectangle | r_x = 1/2 sqrt(1/6 (2 + sqrt(5))) a r_y = a/(2 sqrt(3)) golden rhombus | r_x = a/sqrt(6 (ϕ^2 + 1)) r_y = a/sqrt(6 (1/ϕ^2 + 1)) half rectangle | r_x = b/(2 sqrt(3)) r_y = a/(2 sqrt(3)) half square | r_x = a/(2 sqrt(3)) r_y = a/(2 sqrt(3)) isosceles trapezoid | r_x = h sqrt((3 a + b)/(6 a + 6 b)) r_y = sqrt(a^2/24 + b^2/24) lozenge | r_x = a/sqrt(6) r_y = 1/2 sqrt(2 + sqrt(2)) a monokite | r_x = 1/2 sqrt(37/6) a r_y = a/(2 sqrt(2)) quarter rectangle | r_x = b/(2 sqrt(3)) r_y = a/(2 sqrt(3)) quarter square | r_x = a/(2 sqrt(3)) r_y = a/(2 sqrt(3)) rectangle | r_x = b/(2 sqrt(3)) r_y = a/(2 sqrt(3)) regular diamond | r_x = a/sqrt(6) r_y = a/sqrt(6) rhombus | r_x = (a sin(θ))/sqrt(6) r_y = (a cos(θ))/sqrt(6) right trapezoid | r_x = sqrt(h_1^2 + h_2^2)/sqrt(6) r_y = (a sqrt((h_1 + 3 h_2)/(h_1 + h_2)))/sqrt(6) square | r_x = a/(2 sqrt(3)) r_y = a/(2 sqrt(3)) inverted isosceles trapezoid | r_x = sqrt(-((3 a + b) ((b - a)^2 - 4 c^2))/(a + b))/(2 sqrt(6)) r_y = sqrt(a^2 + b^2)/(2 sqrt(6))

    golden rectangle | K = 1/3 a^4 ϕ (1 - (192 sum_(n=1)^∞ tanh(1/2 π (2 n - 1) ϕ)/(2 n - 1)^5)/(π^5 ϕ)) rectangle | K = 1/3 a^3 b (1 - (192 a sum_(n=1)^∞ tanh((π b (2 n - 1))/(2 a))/(2 n - 1)^5)/(π^5 b)) square | K = 1/3 a^4 (1 - (192 sum_(n=1)^∞ tanh(1/2 π (2 n - 1))/(2 n - 1)^5)/π^5)

    Distance properties

    diamond | sqrt(a^2 + b^2) | sqrt(a^2 + b^2) | sqrt(a^2 + b^2) | sqrt(a^2 + b^2) golden rectangle | a Ï• | a | a Ï• | a golden rhombus | a | a | a | a half rectangle | a | b/2 | a | b/2 half square | a | a/2 | a | a/2 isosceles trapezoid | b | 1/2 sqrt((a - b)^2 + 4 h^2) | a | 1/2 sqrt((a - b)^2 + 4 h^2) kite | a | b | b | a lozenge | a | a | a | a monokite | sqrt(3) a | a | a | sqrt(3) a parallelogram | b | a | b | a quarter rectangle | a/2 | b/2 | a/2 | b/2 quarter square | a/2 | a/2 | a/2 | a/2 rectangle | a | b | a | b regular diamond | sqrt(2) a | sqrt(2) a | sqrt(2) a | sqrt(2) a rhombus | a | a | a | a right trapezoid | a | h_2 | sqrt(a^2 + (h_2 - h_1)^2) | h_1 square | a | a | a | a trapezoid | b | d | a | c inverted isosceles trapezoid | b | c | a | c

    diamond | p = 4 sqrt(a^2 + b^2) golden rectangle | p = 2 a (Ï• + 1) golden rhombus | p = 4 a half rectangle | p = 2 a + b half square | p = 3 a isosceles trapezoid | p = sqrt((a - b)^2 + 4 h^2) + a + b kite | p = 2 (a + b) lozenge | p = 4 a monokite | p = (2 + 2 sqrt(3)) a parallelogram | p = 2 (a + b) quarter rectangle | p = a + b quarter square | p = 2 a rectangle | p = 2 (a + b) regular diamond | p = 4 sqrt(2) a rhombus | p = 4 a right trapezoid | p = sqrt(a^2 + (h_2 - h_1)^2) + a + h_1 + h_2 square | p = 4 a trapezoid | p = a + b + c + d inverted isosceles trapezoid | p = a + b + 2 c

    diamond | r = (a b)/sqrt(a^2 + b^2) golden rhombus | r = a/sqrt(5) kite | r = (h (sqrt(a^2 - h^2) + sqrt(b^2 - h^2)))/sqrt((sqrt(a^2 - h^2) + sqrt(b^2 - h^2))^2 + 4 h^2) lozenge | r = a/(2 sqrt(2)) monokite | r = 1/2 (3 - sqrt(3)) a quarter square | r = a/4 regular diamond | r = a/sqrt(2) rhombus | r = a sin(θ) cos(θ) square | r = a/2

    golden rectangle | R = 1/2 a sqrt(Ï•^2 + 1) half rectangle | R = 1/4 sqrt(4 a^2 + b^2) half square | R = (sqrt(5) a)/4 monokite | R = a quarter rectangle | R = 1/4 sqrt(a^2 + b^2) quarter square | R = a/(2 sqrt(2)) rectangle | R = 1/2 sqrt(a^2 + b^2) square | R = a/sqrt(2)

    diamond | 2 max(a, b) golden rectangle | a sqrt(ϕ^2 + 1) golden rhombus | a/sqrt(5/8 - sqrt(5)/8) half rectangle | (sqrt(5) a)/2 half square | (sqrt(5) a)/2 isosceles trapezoid | max(b, 1/2 sqrt((a + b)^2 + 4 h^2)) kite | max(a, b, 2 h, sqrt(a^2 - h^2) + sqrt(b^2 - h^2)) lozenge | sqrt(2 + sqrt(2)) a monokite | 2 a parallelogram | max(sqrt(a^2 - 2 a b cos(A) + b^2), sqrt(a^2 + 2 a b cos(A) + b^2)) quarter rectangle | 1/2 sqrt(a^2 + b^2) quarter square | a/sqrt(2) rectangle | sqrt(a^2 + b^2) regular diamond | 2 a rhombus | 2 a max(cos(θ), sin(θ)) right trapezoid | max(sqrt(a^2 + h_1^2), sqrt(a^2 + h_2^2)) square | sqrt(2) a trapezoid | max(b, sqrt((a^2 b - a b^2 + a d^2 - b c^2)/(a - b)), sqrt((a^2 b - a b^2 + a c^2 - b d^2)/(a - b))) inverted isosceles trapezoid | max(b, sqrt(a b + c^2))

    diamond | χ = 1 golden rectangle | χ = 1 golden rhombus | χ = 1 half rectangle | χ = 1 half square | χ = 1 isosceles trapezoid | χ = 1 kite | χ = 1 lozenge | χ = 1 monokite | χ = 1 parallelogram | χ = 1 quarter rectangle | χ = 1 quarter square | χ = 1 rectangle | χ = 1 regular diamond | χ = 1 rhombus | χ = 1 right trapezoid | χ = 1 square | χ = 1 trapezoid | χ = 1 inverted isosceles trapezoid | χ = 1

    monokite | s^_ = 1/6 a (4 + 3 log(3)) square | s^_ = 1/15 a (2 + sqrt(2) + 5 sinh^(-1)(1))

    square | A^_ = (11 a^2)/144

    Common classes

    convex laminae | polygonal laminae | quadrilateral laminae

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