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

Author

Paolo Xausa, Jul 28 2025

Keywords

• nonn
• cons
• easy

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.

Examples

			103.37342428732584861123113591699400755105334133204...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 3..10000
• Wikipedia, Metabiaugmented truncated dodecahedron.
• Wikipedia, Parabiaugmented truncated dodecahedron.

Crossrefs

Cf. A386466 (volume).

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

Programs

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]]

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.