A102208 -id:A102208 - cp's OEIS frontend

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

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.

A364897 Decimal expansion of the 4-volume of the unit regular 600-cell.

Original entry on oeis.org

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

Offset: 2

Jianing Song, Aug 12 2023

Decimal expansion of (50+25*sqrt(5))/4.

			Equals 26.47542485937368560255...

Wikipedia, 600-cell
Polytope Wiki, Hexacosichoron

Decimal expansion of 4-volumes: A364895 (5-cell), A000007 = 1 (8-cell or tesseract), A020793 = 1/6 (16-cell), A000038 = 2 (24-cell), A364896 (120-cell), this sequence (600-cell).

Cf. A102208 (decimal expansion of the volume of the unit regular icosahedron).

First[RealDigits[(50 + 25*Sqrt[5])/4, 10, 100]] (* Paolo Xausa, Jun 12 2024 *)

PARI
```
(50+25*sqrt(5))/4
```

A179453 Decimal expansion of the inradius of an icosidodecahedron with edge length 1.

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 14 2010

Icosidodecahedron: 32 faces, 30 vertices, and 60 edges.

			1.46352549156242113615344012577422858829023188485432214660158646702894...

Icosidodecahedron

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452.

Mathematica
```
RealDigits[N[(5+3*Sqrt[5])/8,200]]
```

(sqrt(45)+5)/8 \\ Charles R Greathouse IV, Apr 25 2016

Digits of (5+3*sqrt(5))/8.

cp's OEIS Frontend

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

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

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A364897 Decimal expansion of the 4-volume of the unit regular 600-cell.

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A179453 Decimal expansion of the inradius of an icosidodecahedron with edge length 1.

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