A386412 -id:A386412 - cp's OEIS frontend

A386411 Decimal expansion of the volume of an augmented truncated tetrahedron with unit edge.

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

Offset: 1

Paolo Xausa, Jul 21 2025

The augmented truncated tetrahedron is Johnson solid J_65.

			3.889087296526011384204643991576669716066597657...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Augmented truncated tetrahedron.

Cf. A386412 (surface area).

Cf. A010466, A020829, A377275.

First[RealDigits[11/Sqrt[8], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J65", "Volume"], 10, 100]]

Equals 11/(2*sqrt(2)) = 11/A010466.
Equals A377275 + 10*A020829.
Equals the largest root of 8*x^2 - 121.

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

Original entry on oeis.org

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.

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

Original entry on oeis.org

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.

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A386411 Decimal expansion of the volume of an augmented truncated tetrahedron with unit edge.

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

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

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