平行于立方体的面对角线作6个圆柱，求交集的体积

hbghlyj

1. cyls = {{0, 1/Sqrt[2], 1/Sqrt[2]}, {0, -(1/Sqrt[2]), 1/Sqrt[2]}, {1/Sqrt[2], 0, 1/Sqrt[2]}, {-(1/Sqrt[2]), 0, 1/Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2], 0}, {-(1/Sqrt[2]), 1/Sqrt[2], 0}};
2. Graphics3D[cyl = Cylinder[3 {-#, #}] & /@ cyls]

复制代码

\[V=\dfrac{16}{3}\left(3+2\sqrt3-4\sqrt2\right)\]
36个曲面,其中24个是筝形的,12个是菱形的(Moore 1974).

hbghlyj

1. ineq = 2 x^2 + (y - z)^2 < 2 && 2 x^2 + (y + z)^2 < 2 && 2 (-1 + y^2) + (x - z)^2 < 0 && 2 y^2 + (x + z)^2 < 2 && (x - y)^2 + 2 (-1 + z^2) < 0 && (x + y)^2 + 2 z^2 < 2; With[{h = 1.2},RegionPlot3D[ineq, {x, -h, h}, {y, -h, h}, {z, -h, h}, Boxed -> False, Axes -> None, PlotPoints -> 75, Mesh -> None]]

复制代码