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 1-3 of 3 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.

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.

A387189 Decimal expansion of the smallest dihedral angle, in radians, in a pentagonal bipyramid (Johnson solid J_13).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 21 2025

Keywords

Comments

This is the dihedral angle between triangular faces at the edge where the two pyramidal parts of the solid meet.
Also the dihedral angle between triangular faces in a pentagonal orthobicupola (Johnson solid J_30).

Examples

			1.3047162795687363719907812632876451487306158399...

Links

Crossrefs

Cf. A236367 (J_13 smallest dihedral angle).
Cf. other J_30 dihedral angles: A105199, A377995, A377996.
Cf. A179641 (J_13 volume), A120011 (J_13 surface area, divided by 10).
Cf. A384624 (J_30 volume), A384625 (J_30 surface area).
Cf. A010532, A386852.

Programs

  • Mathematica
    First[RealDigits[ArcCos[(Sqrt[80] - 5)/15], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J13", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos((4*sqrt(5) - 5)/15) = arccos((A010532 - 5)/15).
Equals 2*A386852.
Showing 1-3 of 3 results.

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