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.

A378205 Decimal expansion of the volume of a triakis tetrahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 20 2024

Keywords

Comments

The triakis tetrahedron is the dual polyhedron of the truncated tetrahedron.

Examples

			0.9820927516479826727789505029234014434511610245673...

Links

Crossrefs

Cf. A378204 (surface area), A378206 (inradius), A378207 (midradius), A378208 (dihedral angle).
Cf. A377275 (volume of a truncated tetrahedron with unit edge).
Cf. A002193.

Programs

  • Mathematica
    First[RealDigits[25/36*Sqrt[2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisTetrahedron", "Volume"], 10, 100]]

Formula

Equals (25/36)*sqrt(2) = (25/36)*A002193.

A378207 Decimal expansion of the midradius of a triakis tetrahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 21 2024

Keywords

Comments

The triakis tetrahedron is the dual polyhedron of the truncated tetrahedron.

Examples

			0.589255650988789603667370301754040866070696614740...

Links

Crossrefs

Cf. A378204 (surface area), A378205 (volume), A378206 (inradius), A378208 (dihedral angle).
Cf. A093577 (midradius of a truncated tetrahedron with unit edge).
Cf. A010524.

Programs

  • Mathematica
    First[RealDigits[5/Sqrt[72], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisTetrahedron", "Midradius"], 10, 100]]
  • PARI
    5/sqrt(72) \\ Charles R Greathouse IV, Feb 11 2025

Formula

Equals 5/(6*sqrt(2)) = 5/A010524.

A378206 Decimal expansion of the inradius of a triakis tetrahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 21 2024

Keywords

Comments

The triakis tetrahedron is the dual polyhedron of the truncated tetrahedron.

Examples

			0.53300179088902608574609433108459844097593504016042...

Links

Crossrefs

Cf. A378204 (surface area), A378205 (volume), A378207 (midradius), A378208 (dihedral angle).
Cf. A010539.

Programs

  • Mathematica
    First[RealDigits[5/Sqrt[88], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisTetrahedron", "Inradius"], 10, 100]]

Formula

Equals 5/(2*sqrt(22)) = 5/A010539.

A378208 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a triakis tetrahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 21 2024

Keywords

Comments

The triakis tetrahedron is the dual polyhedron of the truncated tetrahedron.

Examples

			2.2605713275803962793413578116086559655552841805381...

Links

Crossrefs

Cf. A378204 (surface area), A378205 (volume), A378206 (inradius), A378207 (midradius).
Cf. A137914 and A156546 (dihedral angles of a truncated tetrahedron).

Programs

  • Mathematica
    First[RealDigits[ArcCos[-7/11], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["TriakisTetrahedron", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(-7/11).

A380700 Decimal expansion of the acute vertex angles, in radians, in a triakis tetrahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 30 2025

Keywords

Examples

			0.58568554345715095961775753847751776620036106717164...

Links

Crossrefs

Cf. A380701 (face obtuse angle).
Cf. A378204, A378205, A378206, A378207, A378208.

Programs

  • Mathematica
    First[RealDigits[ArcCos[5/6], 10, 100]]

Formula

Equals arccos(5/6).
Equals (Pi - A380701)/2.

A380701 Decimal expansion of the obtuse vertex angle, in radians, in a triakis tetrahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 30 2025

Keywords

Examples

			1.9702215666754913192271283063244673517964472650318...

Links

Crossrefs

Cf. A380700 (face acute angles).
Cf. A378204, A378205, A378206, A378207, A378208.

Programs

  • Mathematica
    First[RealDigits[ArcCos[-7/18], 10, 100]]

Formula

Equals arccos(-7/18).
Equals Pi - 2*A380700.

A382002 Decimal expansion of the isoperimetric quotient of a triakis tetrahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Mar 16 2025

Keywords

Comments

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

Examples

			0.64583578984055654756565980578430049996817368590574...

Links

Crossrefs

Cf. A378204 (surface area), A378205 (volume).
Cf. A000796, A010468, A381684.

Programs

  • Mathematica
    First[RealDigits[15/22*Pi/Sqrt[11], 10, 100]]

Formula

Equals 36*Pi*A378205^2/(A378204^3).
Equals (15/22)*(Pi/sqrt(11)) = (15/22)*(A000796/A010468).
Showing 1-7 of 7 results.

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