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gptkb:Gabriel's_Horn
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2π∫₁^∞ (1/x)√(1+(-1/x^2)^2) dx
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gptkb:icosahedron
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5√3a²
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gptkb:Cubo
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6a^2
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gptkb:truncated_tetrahedron
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7√3 × a² (where a is edge length)
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gptkb:regular_dodecahedron
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3√25+10√5 × a²
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gptkb:Tetrahedron
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sum of areas of 4 faces
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gptkb:tetrahedron
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A = √3 a^2
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gptkb:Cube
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6a^2
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gptkb:dodecahedron
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3√25+10√5 × a²
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gptkb:regular_octahedron
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2√3 a^2
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gptkb:Euclidean_ball
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A = (2π^{n/2} / Γ(n/2)) r^{n-1}
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gptkb:Cuboids
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2 × (length × width + width × height + height × length)
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gptkb:Torricelli's_trumpet
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2π∫₁^∞ (1/x)√(1+(-1/x^2)^2) dx
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gptkb:rhombic_dodecahedron
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8√2 × a² (where a is edge length)
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gptkb:n-ball
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A_n = n V_n / r
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gptkb:Euclidean_ball_(p=2)
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A = (2 * π^{n/2} / Γ(n/2)) * r^{n-1}
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gptkb:cube_(p=∞)
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6a^2
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gptkb:regular_tetrahedron
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√3 a^2
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gptkb:Spheroid
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Depends on type (oblate or prolate)
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gptkb:Cubes
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6a^2
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