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.

A385257 Decimal expansion of the surface area of a gyroelongated triangular bicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 24 2025

Keywords

Comments

The gyroelongated triangular bicupola is Johnson solid J_44.

Examples

			14.660254037844386467637231707529361834714026269...

Links

Crossrefs

Cf. A385256 (volume).
Cf. A002194, A010527.
Essentially the same of A332133, A375193 and A010527.

Programs

  • Mathematica
    First[RealDigits[6 + 5*Sqrt[3], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J44", "SurfaceArea"], 10, 100]]

Formula

Equals 6 + 5*sqrt(3) = 6 + 5*A002194 = 6 + 10*A010527.
Equals the largest root of x^2 - 12*x - 39.

A385258 Decimal expansion of the volume of a gyroelongated square bicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 26 2025

Keywords

Comments

The gyroelongated square bicupola is Johnson solid J_45.

Examples

			8.1535748336212634025260213162662727026732149...

Links

Crossrefs

Cf. A385259 (surface area).
Cf. A002193, A010466, A179587, A384214, A384287, A385256.

Programs

  • Mathematica
    First[RealDigits[2/3*(3 + 2*# + Sqrt[2*(2 + # + Sqrt[146 + 103*#])]) & [Sqrt[2]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J45", "Volume"], 10, 100]]

Formula

Equals (2/3)*(3 + 2*sqrt(2) + sqrt(2*(2 + sqrt(2) + sqrt(146 + 103*sqrt(2))))) = (2/3)*(3 + A010466 + sqrt(2*(2 + A002193 + sqrt(146 + 103*A002193)))).
Equals the largest real root of 6561*x^8 - 104976*x^7 + 594864*x^6 - 1384128*x^5 - 552096*x^4 + 1569024*x^3 + 246528*x^2 - 119808*x + 4352.

A385260 Decimal expansion of the volume of a gyroelongated pentagonal bicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 27 2025

Keywords

Comments

The gyroelongated pentagonal bicupola is Johnson solid J_46.

Examples

			11.397378512213381124089433093505680212446879503678...

Links

Crossrefs

Cf. A385261 (surface area).
Cf. A002163, A384283, A385256, A385258.

Programs

  • Mathematica
    First[RealDigits[(10 + 8*# + 5*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/6 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J46", "Volume"], 10, 100]]

Formula

Equals (10 + 8*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (10 + 8*A002163 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.
Equals the largest real root of 6561*x^8 - 87480*x^7 + 313470*x^6 + 753300*x^5 - 22424850*x^4 - 84591000*x^3 - 85909500*x^2 + 8715000*x + 35547500.

A387294 Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated triangular cupola (Johnson solid J_22).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 25 2025

Keywords

Comments

This is the dihedral angle between a triangular face in the antiprism part of the solid and a triangular face in the cupola part of the solid.
Also the analogous dihedral angle in a gyroelongated triangular bicupola (Johnson solid J_44).

Examples

			2.9570800796354481515618725813450376530518087004...

Links

Crossrefs

Cf. other J_22 dihedral angles: A195698, A387295, A387296, A387297.
Cf. A344076 (J_22 volume), A344077 (J_22 surface area).
Cf. A385256 (J_44 volume), A385257 (J_44 surface area).
Cf. A137914, A246724.

Programs

  • Mathematica
    First[RealDigits[ArcSec[3] + ArcCos[1 - Sqrt[12]/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J22", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(1/3) + arccos(1 - 2*sqrt(3)/3) = A137914 + arccos(-A246724).

A387295 Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated triangular cupola (Johnson solid J_22).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 25 2025

Keywords

Comments

This is the dihedral angle between a triangular face in the antiprism part of the solid and a square face in the cupola part of the solid.
Also the analogous dihedral angle in a gyroelongated triangular bicupola (Johnson solid J_44).

Examples

			2.6814372804191827475908005056128080315848833860639...

Links

Crossrefs

Cf. other J_22 dihedral angles: A195698, A387294, A387296, A387297.
Cf. A344076 (J_22 volume), A344077 (J_22 surface area).
Cf. A385256 (J_44 volume), A385257 (J_44 surface area).
Cf. A195696, A246724.

Programs

  • Mathematica
    First[RealDigits[ArcTan[Sqrt[2]] + ArcCos[1 - Sqrt[12]/3], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J22", "DihedralAngles"]], 2], 10, 100]]

Formula

Equals arccos(sqrt(3)/3) + arccos(1 - 2*sqrt(3)/3) = A195696 + arccos(-A246724).

A387296 Decimal expansion of the third largest dihedral angle, in radians, in a gyroelongated triangular cupola (Johnson solid J_22).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 26 2025

Keywords

Comments

This is the dihedral angle between triangular faces in the antiprism part of the solid.
Also the analogous dihedral angle in a gyroelongated triangular bicupola (Johnson solid J_44).

Examples

			2.5346001497151261930915028102102107021498303291935...

Links

Crossrefs

Cf. other J_22 dihedral angles: A195698, A387294, A387295, A387297.
Cf. A344076 (J_22 volume), A344077 (J_22 surface area).
Cf. A385256 (J_44 volume), A385257 (J_44 surface area).
Cf. A010469.

Programs

  • Mathematica
    First[RealDigits[ArcCos[(1 - Sqrt[12])/3], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J22", "DihedralAngles"]], 3], 10, 100]]

Formula

Equals arccos((1 - 2*sqrt(3))/3) = arccos((1 - A010469)/3).

A385262 Decimal expansion of the volume of a gyroelongated pentagonal cupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 27 2025

Keywords

Comments

The gyroelongated pentagonal cupolarotunda is Johnson solid J_47.

Examples

			15.991096162004890063062980011720804055694009940053...

Links

Crossrefs

Cf. A385263 (surface area).
Cf. A002163, A384283, A385256, A385258, A385260.

Programs

  • Mathematica
    First[RealDigits[5/12*(11 + 5*# + 2*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)]) & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J47", "Volume"], 10, 100]]

Formula

Equals (5/12)*(11 + 5*sqrt(5) + 2*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1))) = (5/12)*(11 + 5*A002163 + 2*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1))).
Equals the largest real root of 1679616*x^8 - 61585920*x^7 + 851472000*x^6 - 5108832000*x^5 + 4745790000*x^4 + 21346200000*x^3 - 29019375000*x^2 - 4576875000*x - 405859375.
Showing 1-7 of 7 results.

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