A386002 Decimal expansion of the volume of an augmented tridiminished icosahedron with unit edge.

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

Offset: 1

Author

Paolo Xausa, Jul 18 2025

Keywords

• nonn
• cons
• easy

Comments

The augmented tridiminished icosahedron is Johnson solid J_64.

Examples

			1.3950376236351965821861497137307637418843196778...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Augmented tridiminished icosahedron.

Crossrefs

Cf. A386003 (surface area).

Cf. A002163, A010466, A020829, A102208, A179552, A385857, A386000.

Programs

Mathematica

First[RealDigits[(15 + Sqrt[8] + 7*Sqrt[5])/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J64", "Volume"], 10, 100]]

Formula

Equals (15 + 2*sqrt(2) + 7*sqrt(5))/24 = (15 + A010466 + 7*A002163)/24.

Equals A102208 - 3*A179552 + A020829 = A386000 + A020829.

Equals the largest root of 2304*x^4 - 5760*x^3 + 3376*x^2 + 280*x - 49.