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 1-8 of 8 results.

A378824 Decimal expansion of the volume of a pentagonal icositetrahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 09 2024

Keywords

Comments

The pentagonal icositetrahedron is the dual polyhedron of the snub cube.

Examples

			35.63020201207128322396774163519636903538669152186...

Links

Crossrefs

Cf. A378823 (surface area), A378825 (inradius), A378826 (midradius), A378827 (dihedral angle).
Cf. A377603 (volume of a snub cube with unit edge length).
Cf. A058265.

Programs

  • Mathematica
    First[RealDigits[Root[#^6 - 1269*#^4 - 649*#^2 - 121 &, 2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalIcositetrahedron", "Volume"], 10, 100]]

Formula

Equals 4*(1 + s)^3*(2 + 3*s)*sqrt(1 - 2*s)/((1 + s)*(1 - 4*s^2)), where s = (A058265 - 1)/2.
Equals the positive real root of x^6 - 1269*x^4 - 649*x^2 - 121.

A378825 Decimal expansion of the inradius of a pentagonal icositetrahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 10 2024

Keywords

Comments

The pentagonal icositetrahedron is the dual polyhedron of the snub cube.

Examples

			1.9506813317847548164887595110561081631709896421193...

Links

Crossrefs

Cf. A378823 (surface area), A378824 (volume), A378826 (midradius), A378827 (dihedral angle).
Cf. A058265.

Programs

  • Mathematica
    First[RealDigits[Root[448*#^6 - 1712*#^4 + 28*#^2 - 1 &, 2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalIcositetrahedron", "Inradius"], 10, 100]]

Formula

Equals (1 + s)/(2*sqrt((1 - 2*s)*(1 - s^2))), where s = (A058265 - 1)/2.
Equals the positive real root of 448*x^6 - 1712*x^4 + 28*x^2 - 1.

A378826 Decimal expansion of the midradius of a pentagonal icositetrahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 10 2024

Keywords

Comments

The pentagonal icositetrahedron is the dual polyhedron of the snub cube.

Examples

			2.101593893296299757309517286375546687971276345216...

Links

Crossrefs

Cf. A378823 (surface area), A378824 (volume), A378825 (inradius), A378827 (dihedral angle).
Cf. A377605 (midradius of a snub cube with unit edge length).
Cf. A058265.

Programs

  • Mathematica
    First[RealDigits[Root[32*#^6 - 144*#^4 + 12*#^2 - 1 &, 2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentagonalIcositetrahedron", "Midradius"], 10, 100]]

Formula

Equals (1 + s)/sqrt(2*(1 + s)*(1 - 2*s)), where s = (A058265 - 1)/2.
Equals the positive real root of 32*x^6 - 144*x^4 + 12*x^2 - 1.

A378827 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentagonal icositetrahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 10 2024

Keywords

Comments

The pentagonal icositetrahedron is the dual polyhedron of the snub cube.

Examples

			2.37904491483881068171953729116462006612803023...

Links

Crossrefs

Cf. A378823 (surface area), A378824 (volume), A378825 (inradius), A378826 (midradius).
Cf. A377969 and A377970 (dihedral angles of a snub cube).

Programs

  • Mathematica
    First[RealDigits[ArcCos[Root[7*#^3 - #^2 - 3*# + 1 &, 1]], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["PentagonalIcositetrahedron", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(c), where c is the real root of 7*x^3 - x^2 - 3*x + 1.

A380775 Decimal expansion of the long/short edge length ratio of a pentagonal icositetrahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 02 2025

Keywords

Examples

			1.419643377607080566275926282326643300212089373...

Links

Crossrefs

Cf. A058265, A378823, A378824, A378825, A378826, A378827, A380776, A380777.

Programs

  • Mathematica
    First[RealDigits[Root[4*#^3 - 8*#^2 + 4*# - 1 &, 1], 10, 100]]

Formula

Equals (A058265 + 1)/2.
Equals the real root of 4*x^3 - 8*x^2 + 4*x - 1.

A380776 Decimal expansion of the acute vertex angle, in radians, in a pentagonal icositetrahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 03 2025

Keywords

Comments

A pentagonal icositetrahedron face is an irregular pentagon with one acute angle (this constant) and four (equal) obtuse angles (A380777).

Examples

			1.409383078032028992695156056940530514142047762023...

Links

Crossrefs

Cf. A058265, A378823, A378824, A378825, A378826, A378827, A380775, A380777.

Programs

  • Mathematica
    First[RealDigits[ArcCos[Root[#^3 - 5*#^2 + 7*# - 1 &, 1]], 10, 100]]

Formula

Equals arccos(2 - A058265).
Equals arccos(c), where c is the real root of x^3 - 5*x^2 + 7*x - 1.
Equals 3*Pi - 4*A380777.

A380777 Decimal expansion of the obtuse vertex angles, in radians, in a pentagonal icositetrahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 03 2025

Keywords

Comments

A pentagonal icositetrahedron face is an irregular pentagon with one acute angle (A380776) and four (equal) obtuse angles (this constant).

Examples

			2.0038487206843376806731935232244945346123651090255...

Links

Crossrefs

Cf. A058265, A378823, A378824, A378825, A378826, A378827, A380775, A380776.

Programs

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

Formula

Equals arccos((1 - A058265)/2).
Equals arccos(c), where c is the real root of 4*x^3 - 4*x^2 + 1.
Equals (3*Pi - A380776)/4.

A382007 Decimal expansion of the isoperimetric quotient of a pentagonal icositetrahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Mar 19 2025

Keywords

Comments

For the definition of isoperimetric quotient of a solid, references and links, see A381684.

Examples

			0.87262832912869975551349997446851467573301874598462...

Links

Crossrefs

Cf. A378823 (surface area), A378824 (volume).
Cf. A000796, A381684.

Programs

  • Mathematica
    First[RealDigits[Pi*Root[1936363968*#^6 - 149531184*#^4 + 10260*#^2 - 1 &, 2], 10, 100]]

Formula

Equals 36*Pi*A378824^2/(A378823^3).
Equals Pi*r = A000796*r, where r is the largest real root of 1936363968*x^6 - 149531184*x^4 + 10260*x^2 - 1.
Showing 1-8 of 8 results.

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