A385804 -id:A385804 - 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.

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.

A386544 Decimal expansion of the volume of a triaugmented truncated dodecahedron with unit edges.

Original entry on oeis.org

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

Offset: 2

Paolo Xausa, Jul 28 2025

The triaugmented truncated dodecahedron is Johnson solid J_71.

			92.01180051437046094749799835011671208159334626...

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

Cf. A386545 (surface area).

Cf. A002163, A179590, A377695, A385506, A385804, A386464, A386466.

First[RealDigits[7/12*(75 + 37*Sqrt[5]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J71", "Volume"], 10, 100]]

Equals (7/12)*(75 + 37*sqrt(5)) = (7/12)*(75 + 37*A002163).
Equals A377695 + 3*A179590.
Equals the largest root of 36*x^2 - 3150*x - 14945.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A386544 Decimal expansion of the volume of a triaugmented truncated dodecahedron with unit edges.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula