A386754 Decimal expansion of the surface area of a triangular hebesphenorotunda with unit edges.

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

Offset: 2

Author

Paolo Xausa, Aug 01 2025

Keywords

• nonn
• cons
• easy

Comments

The triangular hebesphenorotunda is Johnson solid J_92.

Examples

			16.3886735377190679125324060543187225412004474656...
		

Links

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

Crossrefs

Cf. A176324 (volume).

Cf. A002194, A010476.

Programs

Mathematica

First[RealDigits[(12 + 19*A002194 + 3*Sqrt[5*(5 + A010476)])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J92", "SurfaceArea"], 10, 100]]

Formula

Equals (12 + 19*sqrt(3) + 3*sqrt(5*(5 + 2*sqrt(5))))/4 = (12 + 19*A002194 + 3*sqrt(5*(5 + A010476)))/4.

Equals the largest root of 256*x^8 - 6144*x^7 - 19200*x^6 + 1119744*x^5 - 1614816*x^4 - 57096576*x^3 + 76850100*x^2 + 856278216*x + 56001861.