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.

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.

A377602 Decimal expansion of the surface area of a snub cube (snub cuboctahedron) with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 02 2024

Keywords

Examples

			19.856406460551018348219570732046978935542442030...

Links

Crossrefs

Cf. A377603 (volume), A377604 (circumradius), A377605 (midradius).
Cf. A002194, A200243.

Programs

  • Mathematica
    First[RealDigits[6 + Sqrt[192], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["SnubCube", "SurfaceArea"], 10, 100]]

Formula

Equals 6 + 8*sqrt(3) = 6 + 8*A002194 = 6 + A200243.

A377605 Decimal expansion of the midradius of a snub cube (snub cuboctahedron) with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 03 2024

Keywords

Examples

			1.2472231679936432517699189608980305834168701800...

Links

Crossrefs

Cf. A377602 (surface area), A377603 (volume), A377604 (circumradius).
Cf. A058265.

Programs

  • Mathematica
    First[RealDigits[Sqrt[1/(8 - 4*#)], 10, 100]] & [Root[#^3 - #^2 - # - 1 &, 1]] (* or *)
First[RealDigits[PolyhedronData["SnubCube", "Midradius"], 10, 100]]
  • PARI
    polrootsreal(64*x^6 - 112*x^4 + 20*x^2 - 1)[2] \\ Charles R Greathouse IV, Feb 11 2025

Formula

Equals sqrt(1/(4*(2 - A058265))).

A377604 Decimal expansion of the circumradius of a snub cube (snub cuboctahedron) with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 03 2024

Keywords

Examples

			1.343713373744601701271528753975058247637602609...

Links

Crossrefs

Cf. A377602 (surface area), A377603 (volume), A377605 (midradius).
Cf. A058265.

Programs

  • Mathematica
    First[RealDigits[Sqrt[(3 - #)/(8 - 4*#)], 10, 100]] & [Root[#^3 - #^2 - # - 1 &, 1]] (* or *)
First[RealDigits[PolyhedronData["SnubCube", "Circumradius"], 10, 100]]

Formula

Equals sqrt((3 - A058265)/(4*(2 - A058265))).

A377969 Decimal expansion of the dihedral angle, in radians, between triangular faces in a snub cube.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 13 2024

Keywords

Examples

			2.674448083535228681556740855858728640985224997062...

Links

  • Eric Weisstein's World of Mathematics, Snub Cube.

Crossrefs

Cf. A058265, A377602, A377603, A377604, A377605, A377970.

Programs

  • Mathematica
    First[RealDigits[Pi - ArcCos[Root[27*#^3 + 9*#^2 - 15*# - 13 &, 1]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["SnubCube", "DihedralAngles"]], 10, 100]]

Formula

Equals 2*arcsec(sqrt(12*A377604^2 - 3)).
Equals Pi - arccos((2*A058265 - 1)/3).
Equals Pi - arccos(c), where c is the real root of 27*x^3 + 9*x^2 - 15*x - 13.

A377970 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in a snub cube.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 13 2024

Keywords

Examples

			2.4955316305777334348382341626778898107867306036053...

Links

  • Eric Weisstein's World of Mathematics, Snub Cube.

Crossrefs

Cf. A058265, A377602, A377603, A377604, A377605, A377969.

Programs

  • Mathematica
    First[RealDigits[Pi - ArcCos[Root[27*#^6 - 99*#^4 + 129*#^2 - 49 &, 2]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["SnubCube", "DihedralAngles"]], 10, 100]]

Formula

Equals arcsec(sqrt(12*A377604^2 - 3)) + arcsec(sqrt(4*A377604^2 - 1)).
Equals Pi - arccos(sqrt(1 - 2/(3*A058265))).
Equals Pi - arccos(c), where c is the positive real root of 27*x^6 - 99*x^4 + 129*x^2 - 49.

A381690 Decimal expansion of the isoperimetric quotient of a snub cube (snub cuboctahedron).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Mar 06 2025

Keywords

Comments

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

Examples

			0.8991805073406237668693240204602002492109710905019...

Links

Crossrefs

Cf. A377602 (surface area), A377603 (volume).
Cf. A000796, A010502, A381684.

Programs

  • Mathematica
    First[RealDigits[Pi/(3 + Sqrt[48])^3*Root[4*#^3 - 1128*#^2 + 2154*# - 6241 &, 1], 10, 100]]

Formula

Equals 36*Pi*A377603^2/(A377602^3).
Equals (Pi/((3 + 4*sqrt(3))^3))*r = (A000796/((3 + A010502)^3))*r, where r is the real root of 4*x^3 - 1128*x^2 + 2154*x - 6241.
Showing 1-7 of 7 results.

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