A385803 Decimal expansion of the surface area of a parabiaugmented dodecahedron with unit edge.

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

Offset

2,1

Comments

The parabiaugmented dodecahedron is Johnson solid J_59.

Also the surface area of a metabiaugmented dodecahedron (Johnson solid J_60) with unit edge.

Links

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

Wikipedia, Parabiaugmented dodecahedron.

Formula

Equals (5/2)*(sqrt(3) + sqrt(5*(5 + 2*sqrt(5)))) = (5/2)*(A002194 + sqrt(5*(5 + A010476))).

Equals the largest root of x^8 - 700*x^6 + 121250*x^4 - 5421875*x^2 + 390625.

Example

21.5349010248118624614087356276507769114307548346...

Mathematica

First[RealDigits[5/2*(Sqrt[3] + Sqrt[25 + 10*Sqrt[5]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J59", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A385802 (volume).

Cf. A002194, A010476, A385696, A385805.

Sequence in context: A344028 A075303 A076062 * A295563 A395356 A132582

Adjacent sequences: A385800 A385801 A385802 * A385804 A385805 A385806

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 09 2025

Status

approved