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 1-7 of 7 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.

A379891 Decimal expansion of the midradius of a pentagonal hexecontahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 09 2025

Keywords

Comments

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

Examples

			3.59762482255118901142825655944442353841196452...

Links

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379892 (dihedral angle).
Cf. A377807 (midradius of a snub dodecahedron with unit edge length).

Programs

  • Mathematica
    First[RealDigits[Root[4096*#^12 - 58368*#^10 + 70656*#^8 - 17728*#^6 + 1392*#^4 - 120*#^2 + 1 &, 8], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalHexecontahedron", "Midradius"], 10, 100]]

Formula

Equals the largest real root of 4096*x^12 - 58368*x^10 + 70656*x^8 - 17728*x^6 + 1392*x^4 - 120*x^2 + 1.

A380002 Decimal expansion of long/short edge length ratio of a pentagonal hexecontahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 11 2025

Keywords

Examples

			1.749852566736202791676446693655921179649815818590...

Links

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379890 (midradius), A379892 (dihedral angle), A380003 and A380004 (face internal angles).
Cf. A377849.

Programs

  • Mathematica
    First[RealDigits[(1 + #)/(2 - #^2) & [Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1]], 10, 100]] (* or *)
First[RealDigits[1/Divide @@ PolyhedronData["PentagonalHexecontahedron", "EdgeLengths"], 10, 100]]

Formula

Equals (1 + xi)/(2 - xi^2), where xi = A377849.
Equals the largest real root of 31*x^6 - 122*x^5 + 177*x^4 - 128*x^3 + 51*x^2 - 11*x + 1.

A380003 Decimal expansion of acute vertex angle, in radians, in a pentagonal hexecontahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 12 2025

Keywords

Comments

A pentagonal hexecontahedron face is an irregular pentagon with one acute angle (this constant) and four (equal) obtuse angles (A380004).

Examples

			1.1772858234717502919235374454812446809073054345981...

Links

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379890 (midradius), A379892 (dihedral angle), A380002 (long/short edge length ratio), A380004 (face obtuse angles).

Programs

  • Mathematica
    First[RealDigits[ArcCos[Root[64*#^6 - 384*#^5 + 384*#^4 + 888*#^3 + 168*#^2 - 128*# - 31 &, 4]], 10, 100]]

Formula

Equals arccos(c), where c is the largest real root of 64*x^6 - 384*x^5 + 384*x^4 + 888*x^3 + 168*x^2 - 128*x - 31.
Equals 3*Pi - 4*A380004.

A380004 Decimal expansion of obtuse vertex angles, in radians, in a pentagonal hexecontahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 12 2025

Keywords

Comments

A pentagonal hexecontahedron face is an irregular pentagon with one acute angle (A380003) and four (equal) obtuse angles (this constant).

Examples

			2.06187303432440735586609817608931599292105069088...

Links

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379890 (midradius), A379892 (dihedral angle), A380002 (long/short edge length ratio), A380003 (face acute angle).

Programs

  • Mathematica
    First[RealDigits[ArcCos[Root[64*#^6 - 128*#^5 + 64*#^4 + 24*#^3 - 24*#^2 + 1 &, 1]], 10, 100]]

Formula

Equals arccos(c), where c is the smallest real root of 64*x^6 - 128*x^5 + 64*x^4 + 24*x^3 - 24*x^2 + 1.
Equals (3*Pi - A380003)/4.
Showing 1-7 of 7 results.

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