A385695 Decimal expansion of the volume of an augmented dodecahedron with unit edge.

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

Offset

1,1

Comments

The augmented dodecahedron is Johnson solid J_58.

Links

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

Wikipedia, Augmented dodecahedron.

Formula

Equals (95 + 43*sqrt(5))/24 = (95 + 43*A002163)/24.

Equals A102769 + A179552.

Equals the largest root of 144*x^2 - 1140*x - 55.

Example

7.9646217930204565393997694898102032551644412276373...

Mathematica

First[RealDigits[(95 + 43*Sqrt[5])/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J58", "Volume"], 10, 100]]

Crossrefs

Cf. A385696 (surface area).

Cf. A002163, A102769, A179552, A385802, A385804.

Sequence in context: A099877 A197327 A199471 * A200098 A239069 A154168

Adjacent sequences: A385692 A385693 A385694 * A385696 A385697 A385698

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 08 2025

Status

approved