A386543 Decimal expansion of the surface area of a parabiaugmented truncated dodecahedron with unit edges.

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

Offset

3,3

Comments

The parabiaugmented truncated dodecahedron is Johnson solid J_69.

Also the surface area of a metabiaugmented truncated dodecahedron (Johnson solid J_70) with unit edges.

Links

Paolo Xausa, Table of n, a(n) for n = 3..10000

Wikipedia, Metabiaugmented truncated dodecahedron.

Wikipedia, Parabiaugmented truncated dodecahedron.

Formula

Equals (20 + 15*sqrt(3) + 50*sqrt(5 + 2*sqrt(5)) + sqrt(5*(5 + 2*sqrt(5))))/2 = (20 + 15*A002194 + 50*sqrt(5 + A010476) + sqrt(5*(5 + A010476)))/2.

Equals the largest root of x^8 - 80*x^7 - 11400*x^6 + 796000*x^5 + 31475250*x^4 - 1804610000*x^3 - 8296459375*x^2 + 548931187500*x - 2544044046875.

Example

103.37342428732584861123113591699400755105334133204...

Mathematica

First[RealDigits[(20 + 15*Sqrt[3] + 50*Sqrt[#] + Sqrt[5*#])/2 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J69", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A386466 (volume).

Cf. A002194, A010476, A377694, A385803, A386465, A386545.

Sequence in context: A096915 A249806 A249382 * A317929 A385645 A285387

Adjacent sequences: A386540 A386541 A386542 * A386544 A386545 A386546

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 28 2025

Status

approved