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

Author

Paolo Xausa, Jul 09 2025

Keywords

• nonn
• cons
• easy

Comments

The parabiaugmented dodecahedron is Johnson solid J_59.

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

Examples

			21.5349010248118624614087356276507769114307548346...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Parabiaugmented dodecahedron.

Crossrefs

Cf. A385802 (volume).

Cf. A002194, A010476, A385696, A385805.

Programs

Mathematica

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

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.