A385805 Decimal expansion of the surface area of a triaugmented dodecahedron with unit edge.

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

Offset

2,1

Comments

The triaugmented dodecahedron is Johnson solid J_61.

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Wikipedia, Triaugmented dodecahedron.

Formula

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

Equals the largest root of 256*x^8 - 172800*x^6 + 26244000*x^4 - 1230187500*x^2 + 8303765625.

Example

21.97948713368399215555903157714450777070188723...

Mathematica

First[RealDigits[3/4*(5*Sqrt[3] + 3*Sqrt[25 + 10*Sqrt[5]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J61", "SurfaceArea"], 10, 100]]

Crossrefs

Cf. A385804 (volume).

Cf. A002194, A010476, A385696, A385803.

Sequence in context: A016632 A176400 A021459 * A133169 A133175 A188659

Adjacent sequences: A385802 A385803 A385804 * A385806 A385807 A385808

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 09 2025

Status

approved