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.

A378973 Decimal expansion of the surface area of a triakis icosahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 13 2024

Keywords

Comments

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

Examples

			26.228595976743751681458195104356801731865266699519...

Links

Crossrefs

Cf. A378974 (volume), A378975 (inradius), A378976 (midradius), A378977 (dihedral angle).
Cf. A377694 (surface area of a truncated dodecahedron with unit edge length).
Cf. A002163.

Programs

  • Mathematica
    First[RealDigits[3*Sqrt[(173 - 9*Sqrt[5])/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "SurfaceArea"], 10, 100]]

Formula

Equals 3*sqrt((173 - 9*sqrt(5))/2) = 3*sqrt((173 - 9*A002163)/2).

A378974 Decimal expansion of the volume of a triakis icosahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 14 2024

Keywords

Comments

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

Examples

			12.017220926874316513329814423376647765182009668737...

Links

Crossrefs

Cf. A378973 (surface area), A378975 (inradius), A378976 (midradius), A378977 (dihedral angle).
Cf. A377695 (volume of a truncated dodecahedron with unit edge length).
Cf. A002163.

Programs

  • Mathematica
    First[RealDigits[(19 + 13*Sqrt[5])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "Volume"], 10, 100]]

Formula

Equals (19 + 13*sqrt(5))/4 = (19 + 13*A002163)/4.

A378976 Decimal expansion of the midradius of a triakis icosahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 14 2024

Keywords

Comments

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

Examples

			1.3944271909999158785636694674925104941762473438446...

Links

Crossrefs

Cf. A378973 (surface area), A378974 (volume), A378975 (inradius), A378977 (dihedral angle).
Cf. A377697 (midradius of a truncated dodecahedron with unit edge length).
Cf. A002163, A010532, A249600.

Programs

  • Mathematica
    First[RealDigits[1/2 + 2/Sqrt[5], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "Midradius"], 10, 100]]

Formula

Equals 1/2 + 2/sqrt(5) = 1/2 + 2/A002163.
Equals (A249600 + 13)/10 = (A010532 + 5)/10.

A378975 Decimal expansion of the inradius of a triakis icosahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 14 2024

Keywords

Comments

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

Examples

			1.37451744701047164727510000639742367448102733307...

Links

Crossrefs

Cf. A378973 (surface area), A378974 (volume), A378976 (midradius), A378977 (dihedral angle).
Cf. A002163.

Programs

  • Mathematica
    First[RealDigits[Sqrt[(477 + 199*Sqrt[5])/488], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisIcosahedron", "Inradius"], 10, 100]]

Formula

Equals sqrt((477 + 199*sqrt(5))/488) = sqrt((477 + 199*A002163)/488).

A380793 Decimal expansion of the acute vertex angles, in radians, in a triakis icosahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 04 2025

Keywords

Comments

A triakis icosahedron face is an isoscele triangle with two acute angles (this constant) and one obtuse angle (A380794).

Examples

			0.5319820207419660956392085612923249382641913791392...

Links

Crossrefs

Cf. A001622, A378973, A378974, A378976, A378977, A380794.

Programs

  • Mathematica
    First[RealDigits[ArcCos[(GoldenRatio + 7)/10], 10, 100]]

Formula

Equals arccos((A001622 + 7)/10).
Equals (Pi - A380794)/2.

A380794 Decimal expansion of the obtuse vertex angle, in radians, in a triakis icosahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Feb 04 2025

Keywords

Comments

A triakis icosahedron face is an isoscele triangle with two acute angles (A380793) and one obtuse angle (this constant).

Examples

			2.077628612105861047184226260694853007668786641...

Links

Crossrefs

Cf. A001622, A378973, A378974, A378976, A378977, A380793.

Programs

  • Mathematica
    First[RealDigits[ArcCos[-3*GoldenRatio/10], 10, 100]]

Formula

Equals arccos(-3*A001622/10).
Equals Pi - 2*A380793.

A383955 Decimal expansion of sqrt(5/3 - 2*sqrt(1/45)).

Original entry on oeis.org

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

Views

Author

Peter Kagey, Aug 19 2025

Keywords

Comments

Let v_10 be a degree-10 vertex and v_3 be a degree-3 vertex of a triakis icosahedron centered at the origin. Then this is the ratio of norm(v_10)/norm(v_3).
The minimal polynomial is 45*x^4 - 150*x^2 + 121.
One choice of coordinates for the triakis icosahedron describes a degree-10 vertex of the triakis icosahedron as (0,1,(1+sqrt(5)/2)) and a degree-3 vertex as (5+7*sqrt(5)/22*(1, 1, 1).

Examples

			1.169839420461925922675809622142811611361278...

Links

Crossrefs

Cf. A378973, A378974, A378975, A378976, A378977, A380793, A380794, A382009.

Programs

  • Mathematica
    RealDigits[Sqrt[(25 - 2*Sqrt[5])/15], 10, 100][[1]]
Showing 1-7 of 7 results.

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