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 1-4 of 4 results.

A379888 Decimal expansion of the surface area of a pentagonal hexecontahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 07 2025

Keywords

Comments

The pentagonal hexecontahedron is the dual polyhedron of the snub dodecahedron.

Examples

			162.69896419846662676872582412137959709718223664038...

Links

Crossrefs

Cf. A379889 (volume), A379890 (inradius), A379891 (midradius), A379892 (dihedral angle).
Cf. A377804 (surface area of a snub dodecahedron with unit edge length).
Cf. A001622.

Programs

  • Mathematica
    First[RealDigits[Root[961*#^12 - 33925050*#^10 + 238487439375*#^8 - 374285139187500*#^6 + 215543322643359375*#^4 - 200764566730722656250*#^2 + 19088214930090087890625 &, 8], 10, 100]]  (* or *)
First[RealDigits[PolyhedronData["PentagonalHexecontahedron", "SurfaceArea"], 10, 100]]

Formula

Equals 30*(2 + 3*t)*sqrt(1 - t^2)/(1 - 2*t^2), where t = ((44 + 12*A001622*(9 + sqrt(81*A001622 - 15)))^(1/3) + (44 + 12*A001622*(9 - sqrt(81*A001622 - 15)))^(1/3) - 4)/12.
Equals the largest real root of 961*x^12 - 33925050*x^10 + 238487439375*x^8 - 374285139187500*x^6 + 215543322643359375*x^4 - 200764566730722656250*x^2 + 19088214930090087890625.

A379889 Decimal expansion of the volume of a pentagonal hexecontahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 07 2025

Keywords

Comments

The pentagonal hexecontahedron is the dual polyhedron of the snub dodecahedron.

Examples

			189.78985206688527910632308619447379699106033629736...

Links

Crossrefs

Cf. A379888 (surface area), A379890 (inradius), A379891 (midradius), A379892 (dihedral angle).
Cf. A377805 (volume of a snub dodecahedron with unit edge length).
Cf. A001622.

Programs

  • Mathematica
    First[RealDigits[Root[3936256*#^12 - 143719449600*#^10 + 69717538560000*#^8 - 965464153000000*#^6 - 5195593956250000*#^4 - 6093827421875000*#^2 + 171855712890625 &, 8], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalHexecontahedron", "Volume"], 10, 100]]

Formula

Equals 5*(1 + t)*(2 + 3*t)/((1 - 2*t^2)*sqrt(1 - 2*t)), where t = ((44 + 12*A001622*(9 + sqrt(81*A001622 - 15)))^(1/3) + (44 + 12*A001622*(9 - sqrt(81*A001622 - 15)))^(1/3) - 4)/12.
Equals the largest real root of 3936256*x^12 - 143719449600*x^10 + 69717538560000*x^8 - 965464153000000*x^6 - 5195593956250000*x^4 - 6093827421875000*x^2 + 171855712890625.

A379890 Decimal expansion of the inradius of a pentagonal hexecontahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 07 2025

Keywords

Comments

The pentagonal hexecontahedron is the dual polyhedron of the snub dodecahedron.

Examples

			3.49952784890576408257539390033789827877584936895...

Links

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379891 (midradius), A379892 (dihedral angle).

Programs

  • Mathematica
    First[RealDigits[Root[856064*#^12 - 11107328*#^10 + 7691264*#^8 - 698816*#^6 + 8816*#^4 - 440*#^2 + 1 &, 8], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalHexecontahedron", "Inradius"], 10, 100]]

Formula

Equals the largest real root of 856064*x^12 - 11107328*x^10 + 7691264*x^8 - 698816*x^6 + 8816*x^4 - 440*x^2 + 1.

A379892 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentagonal hexecontahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 10 2025

Keywords

Comments

The pentagonal hexecontahedron is the dual polyhedron of the snub dodecahedron.

Examples

			2.6734732271767846682790703348957917197870317502693...

Links

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379891 (midradius).
Cf. A377997 and A377998 (dihedral angles of a snub dodecahedron).
Cf. A377849.

Programs

  • Mathematica
    First[RealDigits[ArcCos[#/(# - 2)] & [Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1]], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["PentagonalHexecontahedron", "DihedralAngles"]], 10, 100]]
  • PARI
    acos(polrootsreal(209*x^6 - 94*x^5 - 137*x^4 + 100*x^3 - 9*x^2 - 6*x + 1)[1]) \\ Charles R Greathouse IV, Feb 10 2025

Formula

Equals arccos(A377849/(A377849 - 2)).
Equals arccos(c), where c is the smallest real root of 209*x^6 - 94*x^5 - 137*x^4 + 100*x^3 - 9*x^2 - 6*x + 1.
Showing 1-4 of 4 results.

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