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 1-6 of 6 results.

A378352 Decimal expansion of the volume of a (small) triakis octahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 23 2024

Keywords

Comments

The (small) triakis octahedron is the dual polyhedron of the truncated cube.

Examples

			2.9142135623730950488016887242096980785696718753769...

Links

Crossrefs

Cf. A378351 (surface area), A378353 (inradius), A201488 (midradius), A378354 (dihedral angle).
Cf. A377299 (volume of a truncated cube with unit edge).
Cf. A156035.
Essentially the same as A002193 and A188582.

Programs

  • Mathematica
    First[RealDigits[Sqrt[2] + 3/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisOctahedron", "Volume"], 10, 100]]

Formula

Equals sqrt(2) + 3/2 = A002193 + 3/2.
Equals A156035/2. - Hugo Pfoertner, Nov 24 2024

A378353 Decimal expansion of the inradius of a (small) triakis octahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 23 2024

Keywords

Comments

The (small) triakis octahedron is the dual polyhedron of the truncated cube.

Examples

			0.81914066340325716171549134573565316624155520306132...

Crossrefs

Cf. A378351 (surface area), A378352 (volume), A201488 (midradius), A378354 (dihedral angle).
Cf. A010487.

Programs

  • Mathematica
    First[RealDigits[Sqrt[23/68 + Sqrt[32]/17], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisOctahedron", "Inradius"], 10, 100]]

Formula

Equals sqrt(23/68 + 4*sqrt(2)/17) = sqrt(23/68 + A010487/17).

A378354 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a (small) triakis octahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 24 2024

Keywords

Comments

The (small) triakis octahedron is the dual polyhedron of the truncated cube.

Examples

			2.57174440034566846791285405092806379355115694111...

Links

Crossrefs

Cf. A378351 (surface area), A378352 (volume), A378353 (inradius), A201488 (midradius).
Cf. A019669 and A195698 (dihedral angles of a truncated cube).
Cf. A377342.

Programs

  • Mathematica
    First[RealDigits[ArcCos[-(3 + 8*Sqrt[2])/17], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["TriakisOctahedron", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(-(3 + 8*sqrt(2))/17) = arccos(-(3 + A377342)/17).

A380702 Decimal expansion of the acute vertex angles, in radians, in a (small) triakis octahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 30 2025

Keywords

Examples

			0.54802840762031274453086328282062867847971236365920...

Links

Crossrefs

Cf. A380703 (face obtuse angle).
Cf. A020765, A361601, A378351, A378352, A378353, A378354.

Programs

  • Mathematica
    First[RealDigits[ArcCos[1/2 + Sqrt[2]/4], 10, 100]]

Formula

Equals arccos(1/2 + sqrt(2)/4) = arccos(1/2 + A020765).
Equals (Pi - A380703)/2.
Equals A361601/2. - Hugo Pfoertner, Jan 30 2025

A380703 Decimal expansion of the obtuse vertex angle, in radians, in a (small) triakis octahedron face.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jan 30 2025

Keywords

Examples

			2.045535838349167749400916817638245527237744672...

Links

Crossrefs

Cf. A380702 (face obtuse angles).
Cf. A010503, A378351, A378352, A378353, A378354.

Programs

  • Mathematica
    First[RealDigits[ArcCos[1/4 - Sqrt[2]/2], 10, 100]]

Formula

Equals arccos(1/4 - sqrt(2)/2) = arccos(1/2 + A010503).
Equals Pi - 2*A380702.

A382003 Decimal expansion of the isoperimetric quotient of a (small) triakis octahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Mar 17 2025

Keywords

Comments

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

Examples

			0.7900283767370127247375294315310284623115183154...

Links

Crossrefs

Cf. A378351 (surface area), A378352 (volume).
Cf. A000796, A002193, A381684.

Programs

  • Mathematica
    First[RealDigits[Pi/51*Sqrt[(1399 + 988*Sqrt[2])/17], 10, 100]]

Formula

Equals 36*Pi*A378352^2/(A378351^3).
Equals (Pi/51)*sqrt((1399 + 988*sqrt(2))/17) = (A000796/51)*sqrt((1399 + 988*A002193)/17).
Showing 1-6 of 6 results.

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