A386460 -id:A386460 - cp's OEIS frontend

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

Paolo Xausa, Jul 25 2025

The augmented truncated dodecahedron is Johnson solid J_68.

			102.18209222021391857798854245281533205298421595361...

Paolo Xausa, Table of n, a(n) for n = 3..10000
Wikipedia, Augmented truncated dodecahedron.

Cf. A386464 (volume).

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

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

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.

A386459 Decimal expansion of the volume of an augmented truncated cube with unit edges.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jul 22 2025

The augmented truncated cube is Johnson solid J_66.

			15.5424723326565069269423398624517230857049...

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

Cf. A386460 (surface area).

Cf. A131594, A179587, A377299, A386411.

First[RealDigits[8 + 16*Sqrt[2]/3, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J66", "Volume"], 10, 100]]

Equals 8 + 16*sqrt(2)/3 = 8 + 16*A131594.
Equals A377299 + A179587.
Equals the largest root of 9*x^2 - 144*x + 64.

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

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

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A386459 Decimal expansion of the volume of an augmented truncated cube with unit edges.

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

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