A378825 Decimal expansion of the inradius of a pentagonal icositetrahedron with unit shorter edge length.

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

Offset

1,2

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

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

Equals the positive real root of 448*x^6 - 1712*x^4 + 28*x^2 - 1.

Example

1.9506813317847548164887595110561081631709896421193...

Mathematica

First[RealDigits[Root[448*#^6 - 1712*#^4 + 28*#^2 - 1 &, 2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalIcositetrahedron", "Inradius"], 10, 100]]

Crossrefs

Cf. A378823 (surface area), A378824 (volume), A378826 (midradius), A378827 (dihedral angle).

Cf. A058265.

Sequence in context: A199509 A266558 A199869 * A197378 A232738 A201395

Adjacent sequences: A378822 A378823 A378824 * A378826 A378827 A378828

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 10 2024

Status

approved