A386465 Decimal expansion of the surface area of an augmented truncated dodecahedron with unit edges.

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

Offset

3,3

Comments

The augmented truncated dodecahedron is Johnson solid J_68.

Links

Paolo Xausa, Table of n, a(n) for n = 3..10000

Wikipedia, Augmented truncated dodecahedron.

Formula

Equals (20 + 25*sqrt(3) + 110*sqrt(5 + 2*sqrt(5)) + sqrt(5*(5 + 2*sqrt(5))))/4 = (20 + 25*A002194 + 110*sqrt(5 + A010476) + sqrt(5*(5 + A010476)))/4.

Equals the largest root of 256*x^8 - 10240*x^7 - 3955200*x^6 + 122240000*x^5 + 16152924000*x^4 - 343551280000*x^3 - 11461251137500*x^2 + 131995515375000*x + 634637481578125.

Example

102.18209222021391857798854245281533205298421595361...

Mathematica

First[RealDigits[(20 + 25*Sqrt[3] + 110*Sqrt[#] + Sqrt[5*#])/4 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J68", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A386464 (volume).

Cf. A002194, A010476, A377694, A386412, A386460, A386543, A386545.

Sequence in context: A008309 A131175 A066532 * A205397 A020778 A118961

Adjacent sequences: A386462 A386463 A386464 * A386466 A386467 A386468

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 25 2025

Status

approved