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    Reuleaux Tetrahedron

    Example plot

    Example plot

    Alternate name

    spherical tetrahedron

    Equation

    x^2 + y^2 + (z + sqrt(3/2)/2)^2<=a^2 ∧ (x - 1/sqrt(3))^2 + y^2 + (z - 1/(2 sqrt(6)))^2<=a^2 ∧ (x + 1/(2 sqrt(3)))^2 + (y - 1/2)^2 + (z - 1/(2 sqrt(6)))^2<=a^2 ∧ (x + 1/(2 sqrt(3)))^2 + (y + 1/2)^2 + (z - 1/(2 sqrt(6)))^2<=a^2

    Solid properties

    S = a^2 (8 π - 18 cos^(-1)(1/3))

    x^_ = (0, 0, 0)

    V = ((8 π)/3 - 27/4 cos^(-1)(1/3) + sqrt(2)/4) a^3

    Distance properties

    sqrt(7/2 - sqrt(6)) a

    χ = 1

    Property

    convex solids

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