A386459 -id:A386459 - cp's OEIS frontend

A386460 Decimal expansion of the surface area of an augmented truncated cube with unit edges.

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

Offset: 2

Paolo Xausa, Jul 23 2025

The augmented truncated cube is Johnson solid J_66.

			34.33828804643758236859922626661459788652513451520...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Augmented truncated cube.

Cf. A386459 (volume).

Cf. A002193, A010482, A386412, A386461.

First[RealDigits[15 + Sqrt[200] + Sqrt[27], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J66", "SurfaceArea"], 10, 100]]

Equals 15 + 10*sqrt(2) + 3*sqrt(3) = 15 + 10*A002193 + A010482.

Equals the largest root of x^4 - 60*x^3 + 896*x^2 + 120*x - 21596.

A386464 Decimal expansion of the volume of an augmented truncated dodecahedron with unit edges.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jul 25 2025

The augmented truncated dodecahedron is Johnson solid J_68.

			87.3637098777040746856191001251416771010058551...

Paolo Xausa, Table of n, a(n) for n = 2..10000
Wikipedia, Augmented truncated dodecahedron.

Cf. A386465 (surface area).

Cf. A179590, A204188, A377695, A386411, A386459, A386466, A386544.

First[RealDigits[505/12 + 81/4*Sqrt[5], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J68", "Volume"], 10, 100]]

Equals 505/12 + 81*sqrt(5)/4 = 505/12 + 81*A204188.
Equals A377695 + A179590.
Equals the largest root of 36*x^2 - 3030*x - 10055.

cp's OEIS Frontend

A386460 Decimal expansion of the surface area of an augmented truncated cube with unit edges.

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