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

1,2

Comments

The augmented tridiminished icosahedron is Johnson solid J_64.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Wikipedia, Augmented tridiminished icosahedron.

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.

Example

1.3950376236351965821861497137307637418843196778...

Mathematica

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

Crossrefs

Cf. A386003 (surface area).

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

Sequence in context: A392282 A258580 A021966 * A016675 A265272 A021257

Adjacent sequences: A385999 A386000 A386001 * A386003 A386004 A386005

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 18 2025

Status

approved