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    Pentagram

    Definition

    Defining inequalities

    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

    Alternate names

    five-point star | pentacle | pentalpha | pentangle

    Lamina properties

    (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)))

    10

    a>0

    A = 1/4 sqrt(650 - 290 sqrt(5)) a^2

    x^_ = (0, 0)

    Mechanical properties

    J_x invisible comma x = (41 a^4)/(24 sqrt(13498 + 30182/sqrt(5)))

    J_y invisible comma y = (41 a^4)/(24 sqrt(13498 + 30182/sqrt(5)))

    J_zz = (41 a^4)/(12 sqrt(13498 + 30182/sqrt(5)))

    J_x invisible comma y = 0

    r_x = 1/4 sqrt(11/3 - 7/sqrt(5)) a r_y = 1/4 sqrt(11/3 - 7/sqrt(5)) a

    Distance properties

    a/Ï•^2 | a/Ï•^2 | a/Ï•^2 | a/Ï•^2 | a/Ï•^2 | a/Ï•^2 | a/Ï•^2 | a/Ï•^2 | a/Ï•^2 | a/Ï•^2

    p = 5 (3 - sqrt(5)) a

    R = sqrt(1/10 (5 - sqrt(5))) a

    a

    Classes

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

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