spherical tetrahedron

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

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

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

χ = 1

convex solids