A179552 -id:A179552 - cp's OEIS frontend

A179592 Decimal expansion of the circumradius of pentagonal cupola with edge length 1.

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 19 2010

Pentagonal cupola: 15 vertices, 25 edges, and 12 faces.

			2.232950509415690049500415383249682772934080730579181647457441260...

Wolfram Alpha, Johnson solid 5
Index entries for algebraic numbers, degree 4.

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A019881, A179587, A179588, A179589, A179590, A179591.

Mathematica
```
RealDigits[N[Sqrt[11+4*Sqrt[5]]/2,200]]
```

Digits of sqrt(11+4*sqrt(5))/2.

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

Original entry on oeis.org

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.

A385804 Decimal expansion of the volume of a triaugmented dodecahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 09 2025

The triaugmented dodecahedron is Johnson solid J_61.

			8.56762745781210568076720062887114294145115942427...

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

Cf. A385805 (surface area).

Cf. A010499, A102769, A179552, A377697, A385695, A385802.

First[RealDigits[5/8*(7 + Sqrt[45]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J61", "Volume"], 10, 100]]

Equals (5/8)*(7 + 3*sqrt(5)) = (5/8)*(7 + A010499).
Equals A102769 + 3*A179552.
Equals the largest root of 16*x^2 - 140*x + 25.
Equals A377697^2. - Hugo Pfoertner, Jul 13 2025

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.

A386000 Decimal expansion of the volume of a tridiminished icosahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 14 2025

The tridiminished icosahedron is Johnson solid J_63.

			1.277186493437438661452675653379955568670180...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Tridiminished icosahedron.

Cf. A386001 (surfacea area).

Cf. A002163, A020829, A102208, A179552, A385857, A386002.

First[RealDigits[5/8 + 7*Sqrt[5]/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J63", "Volume"], 10, 100]]

Equals 5/8 + 7*sqrt(5)/24 = 5/8 + 7*A002163/24.
Equals A102208 - 3*A179552 = A386002 - A020829.
Equals the largest root of 144*x^2 - 180*x - 5.

A386002 Decimal expansion of the volume of an augmented tridiminished icosahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 18 2025

The augmented tridiminished icosahedron is Johnson solid J_64.

			1.3950376236351965821861497137307637418843196778...

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

Cf. A386003 (surface area).

Cf. A002163, A010466, A020829, A102208, A179552, A385857, A386000.

First[RealDigits[(15 + Sqrt[8] + 7*Sqrt[5])/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J64", "Volume"], 10, 100]]

Equals (15 + 2*sqrt(2) + 7*sqrt(5))/24 = (15 + A010466 + 7*A002163)/24.
Equals A102208 - 3*A179552 + A020829 = A386000 + A020829.
Equals the largest root of 2304*x^4 - 5760*x^3 + 3376*x^2 + 280*x - 49.

A179639 Decimal expansion of the volume of gyroelongated pentagonal pyramid with edge length 1.

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 21 2010

Gyroelongated pentagonal pyramid: 11 vertices,25 edges,and 16 faces.

			1.88019215822908780282010679244089525495689855152098881326825313369561...

Wolfram Alpha, Johnson solid 11

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A179554, A179587, A179588, A179589, A179590, A179591, A179592, A179593, A179637, A179638.

Mathematica
```
RealDigits[N[(25+9*Sqrt[5])/24,200]]
```

Digits of (25+9*sqrt(5))/24.

A179640 Decimal expansion of the surface area of gyroelongated pentagonal pyramid with edge length 1.

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 21 2010

Gyroelongated pentagonal pyramid: 11 vertices, 25 edges, and 16 faces.

			8.21566792897225677348693575803563097544289387179912568441637087996861...

Wolfram Alpha, Johnson solid 11

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A179554, A179587, A179588, A179589, A179590, A179591, A179592, A179593, A179637, A179638, A179639.

RealDigits[N[Sqrt[5/2*(70+Sqrt[5]+3*Sqrt[75+30*Sqrt[5]])]/2,200]]

Digits of sqrt(5/2*(70+sqrt(5)+3*sqrt(75+30*sqrt(5))))/2.

A179641 Decimal expansion of the volume of pentagonal dipyramid with edge length 1.

Original entry on oeis.org

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

Offset: 0

Vladimir Joseph Stephan Orlovsky, Jul 21 2010

Pentagonal dipyramid: 7 vertices, 15 edges, and 10 faces.

			0.60300566479164914136743113906093968628671819663429381035590810378421...

Wolfram Alpha, Johnson solid 13

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449-A179452, A179552-A179554, A179587-A179593, A179637-A179640.

Mathematica
```
RealDigits[N[(5+Sqrt[5])/12,200]]
```

(sqrt(5)+5)/12 \\ Charles R Greathouse IV, Apr 25 2016

Digits of (5+sqrt(5))/12.

Offset corrected by R. J. Mathar, Aug 15 2010

A385857 Decimal expansion of the volume of a metabidiminished icosahedron with unit edge.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Jul 14 2025

The metabidiminished icosahedron is Johnson solid J_62.

			1.5786893258332632321363912229104254118135394532...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Metabidiminished icosahedron.

Cf. A384625 (surface area + 10).

Cf. A010476, A102208, A179552, A386000, A386002.

First[RealDigits[(5 + Sqrt[20])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J62", "Volume"], 10, 100]]

Equals (5 + 2*sqrt(5))/6 = (5 + A010476)/6.
Equals A102208 - 2*A179552.
Equals the largest root of 36*x^2 - 60*x + 5.

cp's OEIS Frontend

A179592 Decimal expansion of the circumradius of pentagonal cupola with edge length 1.

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

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A385804 Decimal expansion of the volume 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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A386000 Decimal expansion of the volume of a tridiminished icosahedron with unit edge.

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A386002 Decimal expansion of the volume of an augmented tridiminished icosahedron with unit edge.

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A179639 Decimal expansion of the volume of gyroelongated pentagonal pyramid with edge length 1.

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A179640 Decimal expansion of the surface area of gyroelongated pentagonal pyramid with edge length 1.

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