cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A384283 Decimal expansion of the volume of a gyroelongated pentagonal cupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 26 2025

Keywords

Comments

The gyroelongated pentagonal cupola is Johnson solid J_24.

Examples

			9.07333319388018799314998398101816272215313393060...

Links

Crossrefs

Cf. A384284 (surface area).
Cf. A002163, A010532, A179590, A179639, A179641, A384138, A384140, A384144, A384213.

Programs

  • Mathematica
    First[RealDigits[(5 + Sqrt[80] + 5*Sqrt[2*(Sqrt[650 + 290*Sqrt[5]] - Sqrt[5] - 1)])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J24", "Volume"], 10, 100]]
  • PARI
    (5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 \\ Charles R Greathouse IV, Aug 19 2025

Formula

Equals (5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (5 + A010532 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.
Equals the largest real root of 1679616*x^8 - 11197440*x^7 + 27060480*x^6 + 35769600*x^5 - 4456749600*x^4 - 10714248000*x^3 + 3828402000*x^2 + 13859430000*x + 5340175625.

A384144 Decimal expansion of the volume of an elongated pentagonal cupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 22 2025

Keywords

Comments

The elongated pentagonal cupola is Johnson solid J_20.

Examples

			10.0182541612713266373651755525797920503105009319...

Links

Crossrefs

Cf. A179591 (surface area - 10).
Cf. A010476, A010532, A384138, A384140, A384213.

Programs

  • Mathematica
    First[RealDigits[(5 + Sqrt[80] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J20", "Volume"], 10, 100]]

Formula

Equals (5 + 4*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (5 + A010532 + 15*sqrt(5 + A010476))/6.
Equals the largest root of 324*x^4 - 1080*x^3 - 20340*x^2 - 18600*x + 49975.

A384285 Decimal expansion of the volume of a gyroelongated pentagonal rotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 29 2025

Keywords

Comments

The gyroelongated pentagonal rotunda is Johnson solid J_25.

Examples

			13.667050843671696932123530899233286565400264...

Links

Crossrefs

Cf. A384286 (surface area).
Cf. A002163, A179590, A179639, A179641, A384138, A384140, A384144, A384213, A384283.

Programs

  • Mathematica
    First[RealDigits[(45 + 17*# + 10*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/12 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J25", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 10*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/12 = (45 + 17*A002163 + 10*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/12.
Equals the largest real root of 1679616*x^8 - 50388480*x^7 + 603262080*x^6 - 3520972800*x^5 + 5215460400*x^4 + 4128624000*x^3 - 8894943000*x^2 + 3881385000*x - 424924375.

A386530 Decimal expansion of the largest dihedral angle, in radians, in an elongated pentagonal rotunda (Johnson solid J_21).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 22 2025

Keywords

Comments

This is the dihedral angle between a triangular face and a square face (at the edge where the prism and rotunda parts of the solid meet).
Also the analogous dihedral angle in Johnson solids J_40-J_43.

Examples

			2.9528821228062311686815089830968947118603985336982...

Links

Crossrefs

Cf. other J_21 dihedral angles: A019669, A228824, A344075, A387191.
Cf. A384213 (J_21 volume), A179637 (J_21 surface area - 10).
Cf. A002163.

Programs

  • Mathematica
    First[RealDigits[ArcCos[-Sqrt[2*(5 + Sqrt[5])/15]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J21", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(-sqrt(2*(5 + sqrt(5))/15)) = arccos(-sqrt(2*(5 + A002163)/15)).

A387191 Decimal expansion of the second largest dihedral angle, in radians, in an elongated pentagonal rotunda (Johnson solid J_21).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 22 2025

Keywords

Comments

This is the dihedral angle between a square face and a pentagonal face.
Also one of the dihedral angles in Johnson solids J_40-J_43, J_72-J_75, J_77-J_79 and J_82.

Examples

			2.677945044588987122248387151818288482168632345...

Links

Crossrefs

Cf. other J_21 dihedral angles: A019669, A228824, A344075, A386530.
Cf. A384213 (J_21 volume), A179637 (J_21 surface area - 10).
Cf. A010476, A105199.

Programs

  • Mathematica
    First[RealDigits[Pi/2 + ArcTan[2], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J21", "DihedralAngles"]], 2], 10, 100]]

Formula

Equals Pi/2 + arctan(2) = A019669 + A105199.
Equals arccos(-2*sqrt(5)/5) = arccos(-A010476/5).
Showing 1-5 of 5 results.

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