A179593 -id:A179593 - cp's OEIS frontend

A179637 Decimal expansion of the surface area of pentagonal rotunda with edge length 1.

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

Offset: 2

Vladimir Joseph Stephan Orlovsky, Jul 21 2010

Pentagonal rotunda: 20 vertices, 35 edges, and 17 faces.

			22.3472002653941282767984141581886130738180135134316226129799763167102...

Wolfram Alpha, Johnson solid 6

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

RealDigits[N[Sqrt[5*(145+58*Sqrt[5]+2*Sqrt[30*(65+29*Sqrt[5])])]/2,200]]

Digits of sqrt(5*(145+58*sqrt(5)+2*sqrt(30*(65+29*sqrt(5)))))/2.

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

A179638 Decimal expansion of the volume of gyroelongated square pyramid with edge length 1.

Original entry on oeis.org

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

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 21 2010

Gyroelongated square pyramid: 9 vertices, 20 edges, and 13 faces.

			1.19270224223223255906019842837725158155262551828862015707793142188822...

Wolfram Alpha, Johnson solid 10

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

RealDigits[N[(Sqrt[2]+2*Sqrt[4+3*Sqrt[2]])/6,200]]

Digits of (sqrt(2)+2 sqrt(4+3 sqrt(2)))/6.

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

A386853 Decimal expansion of the dihedral angle, in radians, between the 10-gonal face and a triangular face in a pentagonal rotunda (Johnson solid J_6).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Aug 06 2025

			1.38208579601133454945018729145714326976181383401...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Pentagonal rotunda.
Index entries for transcendental numbers.

Cf. A179593 (volume), A179637 (surface area).
Cf. other J_6 dihedral angles: A105199, A344075.
Cf. A010476, A386852.

First[RealDigits[ArcCos[Sqrt[(5 - Sqrt[20])/15]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J6", "DihedralAngles"]], 2], 10, 100]]

acos(sqrt((5 - 2*sqrt(5))/15)) \\ Charles R Greathouse IV, Aug 19 2025

Equals arccos(sqrt((5 - 2*sqrt(5))/15)) = arccos(sqrt((5 - A010476)/15)).

cp's OEIS Frontend

A179637 Decimal expansion of the surface area of pentagonal rotunda with edge length 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A179638 Decimal expansion of the volume of gyroelongated square pyramid with edge length 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A386853 Decimal expansion of the dihedral angle, in radians, between the 10-gonal face and a triangular face in a pentagonal rotunda (Johnson solid J_6).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula