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  2. Regular dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Regular_dodecahedron

    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 ...

  3. Tetrahedron - Wikipedia

    en.wikipedia.org/wiki/Tetrahedron

    There exist tetrahedra having integer-valued edge lengths, face areas and volume. These are called Heronian tetrahedra. One example has one edge of 896, the opposite edge of 990 and the other four edges of 1073; two faces are isosceles triangles with areas of 436 800 and the other two are isosceles with areas of 47 120, while the volume is 124 ...

  4. Rhombic dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombic_dodecahedron

    The surface area A and the volume V of the rhombic dodecahedron with edge length a are: [4] =, =. The rhombic dodecahedron can be viewed as the convex hull of the union of the vertices of a cube and an octahedron where the edges intersect perpendicularly.

  5. Truncated icosahedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_icosahedron

    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.

  6. Rhombicuboctahedron - Wikipedia

    en.wikipedia.org/wiki/Rhombicuboctahedron

    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 ...

  7. Snub disphenoid - Wikipedia

    en.wikipedia.org/wiki/Snub_disphenoid

    The lengths of the five simple closed geodesics on a snub disphenoid with unit-length edges are 2 3 ≈ 3.464 {\displaystyle 2{\sqrt {3}}\approx 3.464} (for the equatorial geodesic), 13 ≈ 3.606 {\displaystyle {\sqrt {13}}\approx 3.606} , 4 {\displaystyle 4} (for the geodesic through the midpoints of opposite edges), 2 7 ≈ 5.292 ...

  8. Octahedron - Wikipedia

    en.wikipedia.org/wiki/Octahedron

    The surface area of a regular octahedron can be ascertained by summing all of its eight equilateral triangles, whereas its volume is twice the volume of a square pyramid; if the edge length is , [11] =, =. The radius of a circumscribed sphere (one that touches the octahedron at all vertices), the radius of an inscribed sphere (one that tangent ...

  9. Small stellated dodecahedron - Wikipedia

    en.wikipedia.org/wiki/Small_stellated_dodecahedron

    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.

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