A385803 -id:A385803 - cp's OEIS frontend

A385802 Decimal expansion of the volume of a parabiaugmented dodecahedron with unit edge.

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

Offset: 1

Paolo Xausa, Jul 09 2025

The parabiaugmented dodecahedron is Johnson solid J_59.

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

			8.266124625416281110083485059340673098307800325954...

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

Cf. A385803 (surface area).

Cf. A002163, A102769, A179552, A385695, A385804.

First[RealDigits[(25 + 11*Sqrt[5])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J59", "Volume"], 10, 100]]

Equals (25 + 11*sqrt(5))/6 = (25 + 11*A002163)/6.
Equals A102769 + 2*A179552.
Equals the largest root of 9*x^2 - 75*x + 5.

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.

A385696 Decimal expansion of the surface area of an augmented dodecahedron with unit edge.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jul 08 2025

The augmented dodecahedron is Johnson solid J_58.

			21.090314915939732767258439678157046052159622437375...

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

Cf. A385695 (volume).

Cf. A002194, A010476, A385803, A385805.

First[RealDigits[(5*Sqrt[3] + 11*Sqrt[25 + 10*Sqrt[5]])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J58", "SurfaceArea"], 10, 100]]

Equals (5*sqrt(3) + 11*sqrt(5*(5 + 2*sqrt(5))))/4 = (5*A002194 + 11*sqrt(5*(5 + A010476)))/4.

Equals the largest root of 256*x^8 - 198400*x^6 + 41204000*x^4 - 1620087500*x^2 + 7460640625.

A386543 Decimal expansion of the surface area of a parabiaugmented truncated dodecahedron with unit edges.

Original entry on oeis.org

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

Offset: 3

Paolo Xausa, Jul 28 2025

The parabiaugmented truncated dodecahedron is Johnson solid J_69.

Also the surface area of a metabiaugmented truncated dodecahedron (Johnson solid J_70) with unit edges.

			103.37342428732584861123113591699400755105334133204...

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

Cf. A386466 (volume).

Cf. A002194, A010476, A377694, A385803, A386465, A386545.

First[RealDigits[(20 + 15*Sqrt[3] + 50*Sqrt[#] + Sqrt[5*#])/2 & [5 + Sqrt[20]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J69", "SurfaceArea"], 10, 100]]

Equals (20 + 15*sqrt(3) + 50*sqrt(5 + 2*sqrt(5)) + sqrt(5*(5 + 2*sqrt(5))))/2 = (20 + 15*A002194 + 50*sqrt(5 + A010476) + sqrt(5*(5 + A010476)))/2.

Equals the largest root of x^8 - 80*x^7 - 11400*x^6 + 796000*x^5 + 31475250*x^4 - 1804610000*x^3 - 8296459375*x^2 + 548931187500*x - 2544044046875.

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A385802 Decimal expansion of the volume 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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A385696 Decimal expansion of the surface area of an augmented dodecahedron with unit edge.

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A386543 Decimal expansion of the surface area of a parabiaugmented truncated dodecahedron with unit edges.

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