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If the edge length of a regular dodecahedron is , the radius of a circumscribed sphere (one that touches the regular dodecahedron at all vertices), the radius of an inscribed sphere (tangent to each of the regular dodecahedron's faces), and the midradius (one that touches the middle of each edge) are: [21] =, =, =. Given a regular dodecahedron ...
The surface area and the volume of the truncated icosahedron of edge length are: [2] = (+ +) = +. The sphericity of a polyhedron describes how closely a polyhedron resembles a sphere. It can be defined as the ratio of the surface area of a sphere with the same volume to the polyhedron's surface area, from which the value is between 0 and 1.
Animated truncation sequence from {5 ⁄ 2, 5} to {5, 5 ⁄ 2}Its convex hull is the regular convex icosahedron.It also shares its edges with the great icosahedron; the compound with both is the great complex icosidodecahedron.
The volume of a rhombicuboctahedron can be determined by slicing it into two square cupolas and one octagonal prism. Given that the edge length a {\displaystyle a} , its surface area and volume is: [ 7 ] A = ( 18 + 2 3 ) a 2 ≈ 21.464 a 2 , V = 12 + 10 2 3 a 3 ≈ 8.714 a 3 . {\displaystyle {\begin{aligned}A&=\left(18+2{\sqrt {3}}\right)a^{2 ...
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Doubling the cube is the construction, using only a straightedge and compass, of the edge of a cube that has twice the volume of a cube with a given edge. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.
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It is generally a good practice to convert it to {} format, but coherency must be respected; that is, such a conversion must be done in a whole article, or at least in a whole section. Moreover, such a conversion must be identified as such in the edit summary, and making other changes in the same edit should be avoided.
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