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.

A384213 Decimal expansion of the volume of an elongated pentagonal rotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 23 2025

Keywords

Comments

The elongated pentagonal rotunda is Johnson solid J_21.

Examples

			14.611971811062835576338722470794915893557631368294...

Links

Crossrefs

Cf. A179637 (surface area - 10).
Cf. A002163, A010476, A384138, A384140, A384144.

Programs

  • Mathematica
    First[RealDigits[(45 + 17*Sqrt[5] + 30*Sqrt[5 + Sqrt[20]])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J21", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 30*sqrt(5 + 2*sqrt(5)))/12 = (45 + 17*A002163 + 30*sqrt(5 + A010476))/12.
Equals the largest real root of 1296*x^4 - 19440*x^3 + 2340*x^2 + 70200*x + 43525.

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.

A384871 Decimal expansion of the volume of a pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 11 2025

Keywords

Comments

The pentagonal orthocupolarotunda is Johnson solid J_32.
Also the volume of a pentagonal gyrocupolarotunda (Johnson solid J_33) with unit edge.

Examples

			9.2418082864578952008524451431901588238346215825240...

Links

Crossrefs

Cf. A384872 (surface area).
Cf. A002163, A384144, A384283, A384285, A384624.

Programs

  • Mathematica
    First[RealDigits[5*(11 + 5*Sqrt[5])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J32", "Volume"], 10, 100]]

Formula

Equals (5/12)*(11 + 5*sqrt(5)) = (5/12)*(11 + 5*A002163).
Equals the largest root of 36*x^2 - 330*x - 25.

A387190 Decimal expansion of the second smallest dihedral angle, in radians, in an elongated pentagonal cupola (Johnson solid J_20).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 22 2025

Keywords

Comments

This is the dihedral angle between adjacent square faces at the edge where the prism and cupola parts of the solid meet.
Also the analogous dihedral angle in Johnson solids J_38-J_41.
Also the dihedral angle between a square face and a decagonal face in Johnson solids J_76-J_83.

Examples

			2.124370685691941870739854421729019962133608522388...

Links

Crossrefs

Cf. other J_20 dihedral angles: A019669, A228824, A377995, A377996, A387147.
Cf. A384144 (J_20 volume), A179591 (J_20 surface area - 10).
Cf. A002163.

Programs

  • Mathematica
    First[RealDigits[ArcCos[-Sqrt[(5 - Sqrt[5])/10]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J20", "DihedralAngles"]], 2], 10, 100]]

Formula

Equals arccos(-sqrt((5 - sqrt(5))/10)) = arccos(-sqrt((5 - A002163)/10)).
Showing 1-5 of 5 results.

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