A378824 Decimal expansion of the volume of a pentagonal icositetrahedron with unit shorter edge length.

3, 5, 6, 3, 0, 2, 0, 2, 0, 1, 2, 0, 7, 1, 2, 8, 3, 2, 2, 3, 9, 6, 7, 7, 4, 1, 6, 3, 5, 1, 9, 6, 3, 6, 9, 0, 3, 5, 3, 8, 6, 6, 9, 1, 5, 2, 1, 8, 6, 4, 6, 1, 7, 7, 5, 8, 4, 3, 8, 4, 6, 6, 6, 0, 6, 6, 9, 5, 8, 4, 6, 7, 4, 7, 4, 0, 6, 1, 5, 3, 0, 1, 0, 9, 8, 8, 4, 0, 5, 6

Offset

2,1

Comments

The pentagonal icositetrahedron is the dual polyhedron of the snub cube.

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Eric Weisstein's World of Mathematics, Pentagonal Icositetrahedron.

Wikipedia, Pentagonal icositetrahedron.

Formula

Equals 4*(1 + s)^3*(2 + 3*s)*sqrt(1 - 2*s)/((1 + s)*(1 - 4*s^2)), where s = (A058265 - 1)/2.

Equals the positive real root of x^6 - 1269*x^4 - 649*x^2 - 121.

Example

35.63020201207128322396774163519636903538669152186...

Mathematica

First[RealDigits[Root[#^6 - 1269*#^4 - 649*#^2 - 121 &, 2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalIcositetrahedron", "Volume"], 10, 100]]

Crossrefs

Cf. A378823 (surface area), A378825 (inradius), A378826 (midradius), A378827 (dihedral angle).

Cf. A377603 (volume of a snub cube with unit edge length).

Cf. A058265.

Sequence in context: A152713 A218802 A378705 * A236101 A203802 A306554

Adjacent sequences: A378821 A378822 A378823 * A378825 A378826 A378827

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 09 2024

Status

approved