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A179296
Decimal expansion of circumradius of a regular dodecahedron with edge length 1.
8
1, 4, 0, 1, 2, 5, 8, 5, 3, 8, 4, 4, 4, 0, 7, 3, 5, 4, 4, 6, 7, 6, 6, 7, 7, 9, 3, 5, 3, 2, 2, 0, 6, 7, 9, 9, 4, 4, 4, 3, 9, 3, 1, 7, 3, 9, 7, 7, 5, 4, 9, 2, 8, 6, 3, 6, 6, 0, 8, 4, 5, 1, 8, 6, 3, 9, 1, 3, 5, 4, 0, 2, 7, 2, 1, 1, 4, 4, 4, 7, 6, 7, 6, 5, 0, 1, 0, 8, 3, 9, 0, 9, 0, 3, 9, 8, 0, 5, 2, 3, 3, 9, 7, 9, 8
OFFSET
1,2
COMMENTS
Dodecahedron: A three-dimensional figure with 12 faces, 20 vertices, and 30 edges.
Appears as a coordinate in a degree-7 quadrature formula on 12 points over the unit circle [Stroud & Secrest]. - R. J. Mathar, Oct 12 2011
FORMULA
Equals (sqrt(3) + sqrt(15))/4 = sqrt((9 + 3*sqrt(5))/8).
The minimal polynomial is 16*x^4 - 36*x^2 + 9. - Joerg Arndt, Feb 05 2014
Equals (sqrt(3)/2) * phi = A010527 * A001622. - Amiram Eldar, Jun 02 2023
EXAMPLE
1.40125853844407354467667793532206799444393173977549286366084518639135...
MATHEMATICA
RealDigits[N[(Sqrt[3]+Sqrt[15])/4, 175]]
CROSSREFS
Cf. Platonic solids circumradii: A010503 (octahedron), A010527 (cube), A019881 (icosahedron), A187110 (tetrahedron). - Stanislav Sykora, Feb 10 2014
Sequence in context: A141277 A198637 A365094 * A196817 A229987 A343953
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved