A385804 Decimal expansion of the volume of a triaugmented dodecahedron with unit edge.

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

Offset: 1

Author

Paolo Xausa, Jul 09 2025

Keywords

• nonn
• cons
• easy

Comments

The triaugmented dodecahedron is Johnson solid J_61.

Examples

			8.56762745781210568076720062887114294145115942427...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Triaugmented dodecahedron.

Crossrefs

Cf. A385805 (surface area).

Cf. A010499, A102769, A179552, A377697, A385695, A385802.

Programs

Mathematica

First[RealDigits[5/8*(7 + Sqrt[45]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J61", "Volume"], 10, 100]]

Formula

Equals (5/8)*(7 + 3*sqrt(5)) = (5/8)*(7 + A010499).

Equals A102769 + 3*A179552.

Equals the largest root of 16*x^2 - 140*x + 25.

Equals A377697^2. - Hugo Pfoertner, Jul 13 2025