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.

A379133 Decimal expansion of the volume of a pentakis dodecahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 16 2024

Keywords

Comments

The pentakis dodecahedron is the dual polyhedron of the truncated icosahedron.

Examples

			13.458569366318714223642964127539153595279924859762...

Links

Crossrefs

Cf. A379132 (surface area), A379134 (inradius), A379135 (midradius), A379136 (dihedral angle).
Cf. A377751 (volume of a truncated icosahedron with unit edge length).
Cf. A002163.

Programs

  • Mathematica
    First[RealDigits[5/36*(41 + 25*Sqrt[5]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["PentakisDodecahedron", "Volume"], 10, 100]]
  • PARI
    (41 + 25*sqrt(5))*5/36 \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals (5/36)*(41 + 25*sqrt(5)) = (5/36)*(41 + 25*A002163).

A377750 Decimal expansion of the surface area of a truncated icosahedron with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 06 2024

Keywords

Examples

			72.60725303413392187893153397383948620117264765443...

Links

Crossrefs

Cf. A377751 (volume), A377752 (circumradius), A205769 (midradius + 1), A377787 (Dehn invariant).
Cf. A010527 (analogous for a regular icosahedron, with offset 1).
Cf. A002163, A002194, A375067.

Programs

  • Mathematica
    First[RealDigits[3*(10*Sqrt[3] + Sqrt[25 + Sqrt[500]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedIcosahedron", "SurfaceArea"], 10, 100]]
  • PARI
    3*(10*sqrt(3) + sqrt(25 + 10*sqrt(5))) \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals 3*(10*sqrt(3) + sqrt(25 + 10*sqrt(5))) = 30*A002194 + 3*sqrt(25 + 10*A002163).
Equals 30*(A002194 + A375067).

A377752 Decimal expansion of the circumradius of a truncated icosahedron with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 07 2024

Keywords

Examples

			2.47801865906761553756640791226630780693649473...

Links

Crossrefs

Cf. A377750 (surface area), A377751 (volume), A205769 (midradius + 1), A377787 (Dehn invariant).
Cf. A019881 (analogous for a regular icosahedron).
Cf. A002163.

Programs

  • Mathematica
    First[RealDigits[Sqrt[58 + 18*Sqrt[5]]/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedIcosahedron", "Circumradius"], 10, 100]]
  • PARI
    sqrt(58 + 18*sqrt(5))/4 \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals sqrt(58 + 18*sqrt(5))/4 = sqrt(58 + 18*A002163)/4.

A381693 Decimal expansion of the isoperimetric quotient of a truncated icosahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Mar 08 2025

Keywords

Comments

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

Examples

			0.90317079253486933111536917369134449479629558352448...

Links

Crossrefs

Cf. A377750 (surface area), A377751 (volume).
Cf. A019679, A002163, A002194, A010476, A381684.

Programs

  • Mathematica
    First[RealDigits[Pi/12*(125 + 43*Sqrt[5])^2/(Sqrt[300] + Sqrt[25 + Sqrt[500]])^3, 10, 100]]

Formula

Equals 36*Pi*A377751^2/(A377750^3).
Equals (Pi/12)*(125 + 43*sqrt(5))^2/((10*sqrt(3) + sqrt(5*(5 + 2*sqrt(5))))^3) = A019679*(125 + 43*A002163)^2/((10*A002194 + sqrt(5*(5 + A010476)))^3).
Showing 1-4 of 4 results.

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