A385535 -id:A385535 - cp's OEIS frontend

A385534 Decimal expansion of the volume of a biaugmented pentagonal prism with unit edge.

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

Offset: 1

Paolo Xausa, Jul 03 2025

The biaugmented pentagonal prism is Johnson solid J_53.

			2.1918819213799986056929082187918422922639314618025...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Biaugmented pentagonal prism.

Cf. A385535 (surface area).

Cf. A002163, A385509.

First[RealDigits[Sqrt[257 + 90*Sqrt[5] + 24*Sqrt[50 + 20*Sqrt[5]]]/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J53", "Volume"], 10, 100]]

Equals sqrt(257 + 90*sqrt(5) + 24*sqrt(50 + 20*sqrt(5)))/12 = sqrt(257 + 90*A002163 + 24*sqrt(50 + 20*A002163))/12.

Equals the largest root of 429981696*x^8 - 3069591552*x^6 + 5343542784*x^4 - 2504731968*x^2 + 10569001.

A386461 Decimal expansion of the surface area of a biaugmented truncated cube with unit edges.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jul 23 2025

The biaugmented truncated cube is Johnson solid J_67.

			36.241911729260269564523295159701074096328596018257...

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

Cf. A010524 (volume - 9).

Cf. A010469, A010487, A010502, A377342, A385535, A386460.

First[RealDigits[18 + 8*Sqrt[2] + Sqrt[48], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J67", "SurfaceArea"], 10, 100]]

Equals 2*(9 + 4*sqrt(2) + 2*sqrt(3)) = 2*(9 + A010487 + A010469) = 18 + A377342 + A010502.

Equals the largest root of x^4 - 72*x^3 + 1592*x^2 - 10656*x - 2672.

cp's OEIS Frontend

A385534 Decimal expansion of the volume of a biaugmented pentagonal prism with unit edge.

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