hexagram | octagram | pentagram | star of Lakshmi

sqrt(3) a + 3 sqrt(3) x + 3 y>=0 and 3 sqrt(3) x<=sqrt(3) a + 3 y and 6 y<=sqrt(3) a or sqrt(3) a + 6 y>=0 and 3 (sqrt(3) x + y)<=sqrt(3) a and sqrt(3) (a + 3 x)>=3 y

-sqrt(5 + 7/sqrt(2))<=(5 sqrt(2) x + 7 x + 2 sqrt(2) y + 3 y)/a<=sqrt(5 + 7/sqrt(2)) and -sqrt(5 + 7/sqrt(2))<=(2 sqrt(2) x + 3 x + 5 sqrt(2) y + 7 y)/a<=sqrt(5 + 7/sqrt(2)) and -sqrt(5 + 7/sqrt(2))<=(2 sqrt(2) x + 3 x - 5 sqrt(2) y - 7 y)/a<=sqrt(5 + 7/sqrt(2)) and -sqrt(5 + 7/sqrt(2))<=(5 sqrt(2) x + 7 x - 2 sqrt(2) y - 3 y)/a<=sqrt(5 + 7/sqrt(2)) or (24 + 17 sqrt(2)) x>=sqrt(58 + 41 sqrt(2)) a + (10 + 7 sqrt(2)) y and sqrt(116 + 82 sqrt(2)) a + (34 + 24 sqrt(2)) y>=2 (7 + 5 sqrt(2)) x and 7 sqrt(2) x + 10 x + 17 sqrt(2) y + 24 y<=sqrt(58 + 41 sqrt(2)) a or 17 sqrt(2) x + 24 x + 7 sqrt(2) y + 10 y>=sqrt(58 + 41 sqrt(2)) a and sqrt(116 + 82 sqrt(2)) a + 2 (7 + 5 sqrt(2)) y>=(34 + 24 sqrt(2)) x and sqrt(58 + 41 sqrt(2)) a + (10 + 7 sqrt(2)) x>=(24 + 17 sqrt(2)) y or 7 sqrt(2) x + 10 x + 17 sqrt(2) y + 24 y>=sqrt(58 + 41 sqrt(2)) a and 24 sqrt(2) x + 34 x + 10 sqrt(2) y + 14 y<=sqrt(116 + 82 sqrt(2)) a and sqrt(58 + 41 sqrt(2)) a + (24 + 17 sqrt(2)) x>=(10 + 7 sqrt(2)) y or (24 + 17 sqrt(2)) y>=sqrt(58 + 41 sqrt(2)) a + (10 + 7 sqrt(2)) x and 10 sqrt(2) x + 14 x + 24 sqrt(2) y + 34 y<=sqrt(116 + 82 sqrt(2)) a and sqrt(58 + 41 sqrt(2)) a + 17 sqrt(2) x + 24 x + 7 sqrt(2) y + 10 y>=0 or (10 + 7 sqrt(2)) y>=sqrt(58 + 41 sqrt(2)) a + (24 + 17 sqrt(2)) x and sqrt(116 + 82 sqrt(2)) a + 2 (7 + 5 sqrt(2)) x>=(34 + 24 sqrt(2)) y and sqrt(58 + 41 sqrt(2)) a + 7 sqrt(2) x + 10 x + 17 sqrt(2) y + 24 y>=0 or sqrt(58 + 41 sqrt(2)) a + 17 sqrt(2) x + 24 x + 7 sqrt(2) y + 10 y<=0 and sqrt(116 + 82 sqrt(2)) a + (34 + 24 sqrt(2)) x>=2 (7 + 5 sqrt(2)) y and sqrt(58 + 41 sqrt(2)) a + (24 + 17 sqrt(2)) y>=(10 + 7 sqrt(2)) x or sqrt(58 + 41 sqrt(2)) a + 7 sqrt(2) x + 10 x + 17 sqrt(2) y + 24 y<=0 and sqrt(116 + 82 sqrt(2)) a + 24 sqrt(2) x + 34 x + 10 sqrt(2) y + 14 y>=0 and sqrt(58 + 41 sqrt(2)) a + (10 + 7 sqrt(2)) y>=(24 + 17 sqrt(2)) x or sqrt(58 + 41 sqrt(2)) a + (24 + 17 sqrt(2)) y<=(10 + 7 sqrt(2)) x and sqrt(116 + 82 sqrt(2)) a + 10 sqrt(2) x + 14 x + 24 sqrt(2) y + 34 y>=0 and 17 sqrt(2) x + 24 x + 7 sqrt(2) y + 10 y<=sqrt(58 + 41 sqrt(2)) a

2 a + 3 sqrt(5) x + 5 x>=sqrt(2 (5 + sqrt(5))) y and 2 a + sqrt(50 + 22 sqrt(5)) y>=(5 + sqrt(5)) x and sqrt(5) a + 2 sqrt(5) x + 2 sqrt(5 + 2 sqrt(5)) y<=a or sqrt(5) a + 2 sqrt(5) x + 2 sqrt(5 + 2 sqrt(5)) y>=a and a + 2 sqrt(5) x<=sqrt(5) a + 2 sqrt(5 + 2 sqrt(5)) y and 2 sqrt(5 + 2 sqrt(5)) y<=a and 3 sqrt(5) x + 5 x + sqrt(2 (5 + sqrt(5))) y<=2 a or a + 2 sqrt(5) x>=sqrt(5) a + 2 sqrt(5 + 2 sqrt(5)) y and 2 a + (5 + sqrt(5)) x + sqrt(50 + 22 sqrt(5)) y>=0 and 3 sqrt(5) x + 5 x + sqrt(2 (5 + sqrt(5))) y<=2 a or sqrt(2/(65 + 29 sqrt(5))) a + sqrt(5) y>=3 y and 3 sqrt(5) x + 5 x + sqrt(2 (5 + sqrt(5))) y>=2 a and sqrt(50 - 22 sqrt(5)) x + y<=2 sqrt(2/(65 + 29 sqrt(5))) a + sqrt(5) y or 2 sqrt(2/(65 + 29 sqrt(5))) a + sqrt(50 - 22 sqrt(5)) x + sqrt(5) y>=y and 2 a + 3 sqrt(5) x + 5 x<=sqrt(2 (5 + sqrt(5))) y or 2 sqrt(5 + 2 sqrt(5)) y>=a and sqrt(650 - 290 sqrt(5)) a + 10 sqrt(5 - 2 sqrt(5)) x + 20 y>=10 sqrt(5) y and 10 (sqrt(5 - 2 sqrt(5)) x + (sqrt(5) - 2) y)<=sqrt(650 - 290 sqrt(5)) a

abs(y)<=a/2 and abs(x)<=a/2 or abs(x - y)<=a/sqrt(2) and abs(x + y)<=a/sqrt(2)

Magen David | Mogen David | shield of David | six-point star | six-pointed star | Solomon's seal | star of David

eight-point star

five-point star | pentacle | pentalpha | pentangle

hexagram | (0, a/sqrt(3)) | (-a/6, a/(2 sqrt(3))) | (-a/2, a/(2 sqrt(3))) | (-a/3, 0) | (-a/2, -a/(2 sqrt(3))) | (-a/6, -a/(2 sqrt(3))) | (0, -a/sqrt(3)) | (a/6, -a/(2 sqrt(3))) | (a/2, -a/(2 sqrt(3))) | (a/3, 0) | (a/2, a/(2 sqrt(3))) | (a/6, a/(2 sqrt(3))) octagram | (0, sqrt(1 - 1/sqrt(2)) a) | (-1/2 sqrt(5 - 7/sqrt(2)) a, 1/2 sqrt(1 - 1/sqrt(2)) a) | (root of 1 - 8 x^2 + 8 x^4 near x = -0.382683 a, 1/2 sqrt(2 - sqrt(2)) a) | (-1/2 sqrt(1 - 1/sqrt(2)) a, 1/2 sqrt(5 - 7/sqrt(2)) a) | (-sqrt(1 - 1/sqrt(2)) a, 0) | (-1/2 sqrt(1 - 1/sqrt(2)) a, -1/2 sqrt(5 - 7/sqrt(2)) a) | (root of 1 - 8 x^2 + 8 x^4 near x = -0.382683 a, root of 1 - 8 x^2 + 8 x^4 near x = -0.382683 a) | (-1/2 sqrt(5 - 7/sqrt(2)) a, -1/2 sqrt(1 - 1/sqrt(2)) a) | (0, -sqrt(1 - 1/sqrt(2)) a) | (1/2 sqrt(5 - 7/sqrt(2)) a, -1/2 sqrt(1 - 1/sqrt(2)) a) | (1/2 sqrt(2 - sqrt(2)) a, root of 1 - 8 x^2 + 8 x^4 near x = -0.382683 a) | (1/2 sqrt(1 - 1/sqrt(2)) a, -1/2 sqrt(5 - 7/sqrt(2)) a) | (sqrt(1 - 1/sqrt(2)) a, 0) | (1/2 sqrt(1 - 1/sqrt(2)) a, 1/2 sqrt(5 - 7/sqrt(2)) a) | (1/2 sqrt(2 - sqrt(2)) a, 1/2 sqrt(2 - sqrt(2)) a) | (1/2 sqrt(5 - 7/sqrt(2)) a, 1/2 sqrt(1 - 1/sqrt(2)) a) pentagram | (a/2, 1/2 sqrt(1 - 2/sqrt(5)) a) | (1/2 (-2 + sqrt(5)) a, 1/2 sqrt(1 - 2/sqrt(5)) a) | (0, root of 1 - 5 x^2 + 5 x^4 near x = 0.525731 a) | ((1 - sqrt(5)/2) a, 1/2 sqrt(1 - 2/sqrt(5)) a) | (-a/2, 1/2 sqrt(1 - 2/sqrt(5)) a) | (1/4 (-3 + sqrt(5)) a, -a/sqrt(130 + 58 sqrt(5))) | (1/4 (1 - sqrt(5)) a, root of 1 - 20 x^2 + 80 x^4 near x = -0.425325 a) | (0, root of 1 - 25 x^2 + 5 x^4 near x = -0.200811 a) | (1/4 (-1 + sqrt(5)) a, root of 1 - 20 x^2 + 80 x^4 near x = -0.425325 a) | (1/4 (3 - sqrt(5)) a, -a/sqrt(130 + 58 sqrt(5))) star of Lakshmi | (0, a/sqrt(2)) | ((1/2 - 1/sqrt(2)) a, a/2) | (-a/2, a/2) | (-a/2, (-1/2 + 1/sqrt(2)) a) | (-a/sqrt(2), 0) | (-a/2, (1/2 - 1/sqrt(2)) a) | (-a/2, -a/2) | ((1/2 - 1/sqrt(2)) a, -a/2) | (0, -a/sqrt(2)) | ((-1/2 + 1/sqrt(2)) a, -a/2) | (a/2, -a/2) | (a/2, (1/2 - 1/sqrt(2)) a) | (a/sqrt(2), 0) | (a/2, (-1/2 + 1/sqrt(2)) a) | (a/2, a/2) | ((-1/2 + 1/sqrt(2)) a, a/2)

hexagram | 12 octagram | 16 pentagram | 10 star of Lakshmi | 16

hexagram | a>0 octagram | a>0 pentagram | a>0 star of Lakshmi | a>0

hexagram | A = a^2/sqrt(3) octagram | A = (6 sqrt(2) - 8) a^2 pentagram | A = 1/4 sqrt(650 - 290 sqrt(5)) a^2 star of Lakshmi | A = 2 (2 - sqrt(2)) a^2

hexagram | x^_ = (0, 0) octagram | x^_ = (0, 0) pentagram | x^_ = (0, 0) star of Lakshmi | x^_ = (0, 0)

hexagram | J_x invisible comma x = (11 a^4)/(216 sqrt(3)) octagram | J_x invisible comma x = ((8 sqrt(2))/3 - 15/4) a^4 pentagram | J_x invisible comma x = (41 a^4)/(24 sqrt(13498 + 30182/sqrt(5))) star of Lakshmi | J_x invisible comma x = 1/12 (7 - 4 sqrt(2)) a^4

hexagram | J_y invisible comma y = (11 a^4)/(216 sqrt(3)) octagram | J_y invisible comma y = ((8 sqrt(2))/3 - 15/4) a^4 pentagram | J_y invisible comma y = (41 a^4)/(24 sqrt(13498 + 30182/sqrt(5))) star of Lakshmi | J_y invisible comma y = 1/12 (7 - 4 sqrt(2)) a^4

hexagram | J_zz = (11 a^4)/(108 sqrt(3)) octagram | J_zz = 1/6 (32 sqrt(2) - 45) a^4 pentagram | J_zz = (41 a^4)/(12 sqrt(13498 + 30182/sqrt(5))) star of Lakshmi | J_zz = 1/6 (7 - 4 sqrt(2)) a^4

hexagram | J_x invisible comma y = 0 octagram | J_x invisible comma y = 0 pentagram | J_x invisible comma y = 0 star of Lakshmi | J_x invisible comma y = 0

hexagram | r_x = 1/6 sqrt(11/6) a r_y = 1/6 sqrt(11/6) a octagram | r_x = 1/4 sqrt(4 - (7 sqrt(2))/3) a r_y = 1/4 sqrt(4 - (7 sqrt(2))/3) a pentagram | r_x = 1/4 sqrt(11/3 - 7/sqrt(5)) a r_y = 1/4 sqrt(11/3 - 7/sqrt(5)) a star of Lakshmi | r_x = 1/4 sqrt(2 - sqrt(2)/3) a r_y = 1/4 sqrt(2 - sqrt(2)/3) a

hexagram | a/3 | a/3 | a/3 | a/3 | a/3 | a/3 | a/3 | a/3 | a/3 | a/3 | a/3 | a/3 octagram | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a | 1/2 (2 - sqrt(2)) a pentagram | a/ϕ^2 | a/ϕ^2 | a/ϕ^2 | a/ϕ^2 | a/ϕ^2 | a/ϕ^2 | a/ϕ^2 | a/ϕ^2 | a/ϕ^2 | a/ϕ^2 star of Lakshmi | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a | (1 - 1/sqrt(2)) a

hexagram | p = 4 a octagram | p = (16 a)/(2 + sqrt(2)) pentagram | p = 5 (3 - sqrt(5)) a star of Lakshmi | p = 8 (2 - sqrt(2)) a

hexagram | R = a/sqrt(3) octagram | R = sqrt(1 - 1/sqrt(2)) a pentagram | R = sqrt(1/10 (5 - sqrt(5))) a star of Lakshmi | R = a/sqrt(2)

hexagram | (2 a)/sqrt(3) octagram | sqrt(4 - 2 sqrt(2)) a pentagram | a star of Lakshmi | sqrt(2) a

concave laminae | equilateral polygonal laminae | polygonal laminae | regular star polygonal laminae