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    Parallelepiped

    Named solids

    cube | cuboid

    Plots

    Plots Cube

    Plots Cuboid

    Alternate names

    solid regular hexahedron

    box | rectangular parallelepiped | rectangular right prism

    Equation

    2 z<=a and 2 x<=a and 2 y<=a and 2 x>=-a and 2 z>=-a and 2 y>=-a

    abs(x)<=a/2 and abs(y)<=b/2 and abs(z)<=c/2

    Solid properties

    | vertices cube | (-a/2, -a/2, -a/2) | (-a/2, -a/2, a/2) | (-a/2, a/2, -a/2) | (-a/2, a/2, a/2) | (a/2, -a/2, -a/2) | (a/2, -a/2, a/2) | (a/2, a/2, -a/2) | (a/2, a/2, a/2) cuboid | (-a/2, -b/2, -c/2) | (-a/2, -b/2, c/2) | (-a/2, b/2, -c/2) | (-a/2, b/2, c/2) | (a/2, -b/2, -c/2) | (a/2, -b/2, c/2) | (a/2, b/2, -c/2) | (a/2, b/2, c/2) | number of vertices cube | 8 cuboid | 8 | height cuboid | c | surface area cube | S = 6 a^2 cuboid | S = 2 (a b + a c + b c) | centroid cube | x^_ = (0, 0, 0) cuboid | x^_ = (0, 0, 0) | volume cube | V = a^3 cuboid | V = a b c | moment of inertia tensor cube | I = (a^2/6 | 0 | 0 0 | a^2/6 | 0 0 | 0 | a^2/6) cuboid | I = (1/12 (b^2 + c^2) | 0 | 0 0 | 1/12 (a^2 + c^2) | 0 0 | 0 | 1/12 (a^2 + b^2))

    Distance properties

    | generalized diameter cube | sqrt(3) a cuboid | sqrt(a^2 + b^2 + c^2) | convexity coefficient cube | χ = 1 cuboid | χ = 1 | mean line segment length cube | s^_ = a Δ(3) cuboid | s^_ = (90 a^2 b^2 sqrt(a^2 + b^2 + c^2) c^2 + 105 a b (sinh^(-1)(c/sqrt(a^2 + b^2)) b a^3 + sinh^(-1)(b/sqrt(a^2 + c^2)) c a^3 + sinh^(-1)(c/sqrt(a^2 + b^2)) b^3 a + sinh^(-1)(b/sqrt(a^2 + c^2)) c^3 a + sinh^(-1)(a/sqrt(b^2 + c^2)) b c^3 + sinh^(-1)(a/sqrt(b^2 + c^2)) b^3 c) c - 84 a b (tan^(-1)((b c)/(a sqrt(a^2 + b^2 + c^2))) a^4 + tan^(-1)((a c)/(b sqrt(a^2 + b^2 + c^2))) b^4 + tan^(-1)((a b)/(c sqrt(a^2 + b^2 + c^2))) c^4) c + 21 (sinh^(-1)(b/a) b a^6 + sinh^(-1)(c/a) c a^6 + sinh^(-1)(a/b) b^6 a + sinh^(-1)(a/c) c^6 a + sinh^(-1)(b/c) b c^6 + sinh^(-1)(c/b) b^6 c) - 21 (sinh^(-1)(b/sqrt(a^2 + c^2)) b a^6 + sinh^(-1)(c/sqrt(a^2 + b^2)) c a^6 + sinh^(-1)(a/sqrt(b^2 + c^2)) b^6 a + sinh^(-1)(a/sqrt(b^2 + c^2)) c^6 a + sinh^(-1)(b/sqrt(a^2 + c^2)) b c^6 + sinh^(-1)(c/sqrt(a^2 + b^2)) b^6 c) + 25 (b^2 (sqrt(a^2 + b^2) - sqrt(a^2 + b^2 + c^2)) a^4 + c^2 (sqrt(a^2 + c^2) - sqrt(a^2 + b^2 + c^2)) a^4 + b^4 (sqrt(a^2 + b^2) - sqrt(a^2 + b^2 + c^2)) a^2 + c^4 (sqrt(a^2 + c^2) - sqrt(a^2 + b^2 + c^2)) a^2 + b^2 c^4 (sqrt(b^2 + c^2) - sqrt(a^2 + b^2 + c^2)) + b^4 c^2 (sqrt(b^2 + c^2) - sqrt(a^2 + b^2 + c^2))) + 8 ((a - sqrt(a^2 + b^2) - sqrt(a^2 + c^2) + sqrt(a^2 + b^2 + c^2)) a^6 + b^6 (b - sqrt(a^2 + b^2) - sqrt(b^2 + c^2) + sqrt(a^2 + b^2 + c^2)) + c^6 (c - sqrt(a^2 + c^2) - sqrt(b^2 + c^2) + sqrt(a^2 + b^2 + c^2))))/(630 a^2 b^2 c^2) | mean tetrahedron volume cube | V^_ = (3977/216000 - π^2/2160) a^3

    Common properties

    convex solids | hexahedra | parallelepipeds | solid polyhedra

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