A385696 -id:A385696 - cp's OEIS frontend

A385803 Decimal expansion of the surface area of a parabiaugmented dodecahedron with unit edge.

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

Offset: 2

Paolo Xausa, Jul 09 2025

The parabiaugmented dodecahedron is Johnson solid J_59.

Also the surface area of a metabiaugmented dodecahedron (Johnson solid J_60) with unit edge.

			21.5349010248118624614087356276507769114307548346...

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

Cf. A385802 (volume).

Cf. A002194, A010476, A385696, A385805.

First[RealDigits[5/2*(Sqrt[3] + Sqrt[25 + 10*Sqrt[5]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J59", "SurfaceArea"], 10, 100]]

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

Equals the largest root of x^8 - 700*x^6 + 121250*x^4 - 5421875*x^2 + 390625.

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

Original entry on oeis.org

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

Paolo Xausa, Jul 09 2025

The triaugmented dodecahedron is Johnson solid J_61.

			21.97948713368399215555903157714450777070188723...

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

Cf. A385804 (volume).

Cf. A002194, A010476, A385696, A385803.

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

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.

A385695 Decimal expansion of the volume of an augmented dodecahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 08 2025

The augmented dodecahedron is Johnson solid J_58.

			7.9646217930204565393997694898102032551644412276373...

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

Cf. A385696 (surface area).

Cf. A002163, A102769, A179552, A385802, A385804.

First[RealDigits[(95 + 43*Sqrt[5])/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J58", "Volume"], 10, 100]]

Equals (95 + 43*sqrt(5))/24 = (95 + 43*A002163)/24.
Equals A102769 + A179552.
Equals the largest root of 144*x^2 - 1140*x - 55.

cp's OEIS Frontend

A385803 Decimal expansion of the surface area of a parabiaugmented dodecahedron with unit edge.

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

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A385695 Decimal expansion of the volume of an augmented dodecahedron with unit edge.

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