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.

User: Paolo Xausa

Paolo Xausa's wiki page.

Paolo Xausa has authored 773 sequences. Here are the ten most recent ones:

A387322 Decimal expansion of the fourth largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 29 2025

Keywords

Comments

This is the dihedral angle between a triangular face and a square face at the edge where the antiprism and cupola parts of the solid meet.
Also the analogous dihedral angle in a gyroelongated square bicupola (Johnson solid J_45).

Examples

			2.4712905456469785754732547961552537994857493330886...

Links

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387321, A387323.
Cf. A384214 (J_23 volume), A384215 (J_23 surface area).
Cf. A385258 (J_45 volume), A385259 (J_45 surface area).
Cf. A003881, A002193, A010487.

Programs

  • Mathematica
    First[RealDigits[Pi/4 + ArcCos[-Sqrt[(7 + Sqrt[32] - 2*Sqrt[20 + 14*Sqrt[2]])/3]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J23", "DihedralAngles"]], 4], 10, 100]]

Formula

Equals Pi/4 + arccos(-sqrt((7 + 4*sqrt(2) - 2*sqrt(20 + 14*sqrt(2)))/3)) = A003881 + arccos(-sqrt((7 + A010487 - 2*sqrt(20 + 14*A002193))/3)).
Equals A003881 + A387323.

A387321 Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 27 2025

Keywords

Comments

This is the dihedral angle between adjacent triangular faces at the edge where the antiprism and cupola parts of the solid meet.
Also the analogous dihedral angle in a gyroelongated square bicupola (Johnson solid J_45).

Examples

			2.6412090003740395440214510528511358326798716782548...

Links

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387322, A387323.
Cf. A384214 (J_23 volume), A384215 (J_23 surface area).
Cf. A385258 (J_45 volume), A385259 (J_45 surface area).
Cf. A002193, A010487, A195696.

Programs

  • Mathematica
    First[RealDigits[ArcSec[Sqrt[3]] + ArcCos[-Sqrt[(7 + Sqrt[32] - 2*Sqrt[20 + 14*Sqrt[2]])/3]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J23", "DihedralAngles"]],2], 10, 100]]

Formula

Equals arcsec(sqrt(3)) + arccos(-sqrt((7 + 4*sqrt(2) - 2*sqrt(20 + 14*sqrt(2)))/3)) = A195696 + arccos(-sqrt((7 + A010487 - 2*sqrt(20 + 14*A002193))/3)).
Equals A195696 + A387323.

A387323 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 29 2025

Keywords

Comments

This is the dihedral angle between a triangular face and the octagonal face.

Examples

			1.6858923822495302658575939503353780784364569832448...

Links

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387321, A387322.
Cf. A384214 (J_23 volume), A384215 (J_23 surface area).
Cf. A002193, A003881, A010487, A195696.

Programs

  • Mathematica
    First[RealDigits[ArcCos[-Sqrt[(7 + Sqrt[32] - 2*Sqrt[20 + 14*Sqrt[2]])/3]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J23", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(-sqrt((7 + 4*sqrt(2) - 2*sqrt(20 + 14*sqrt(2)))/3)) = arccos(-sqrt((7 + A010487 - 2*sqrt(20 + 14*A002193))/3)).
Equals A387321 - A195696 = A387322 - A003881.

A387320 Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 27 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 square bicupola (Johnson solid J_45).

Examples

			2.687150505637070622058237671034217872408094243788...

Links

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387321, A387322, A387323.
Cf. A384214 (J_23 volume), A384215 (J_23 surface area).
Cf. A385258 (J_45 volume), A385259 (J_45 surface area).
Cf. A002193.

Programs

  • Mathematica
    First[RealDigits[ArcCos[(1 - Sqrt[8 + Sqrt[32]])/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J23", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos((1 - 2*sqrt(2 + sqrt(2)))/3) = arccos((1 - 2*sqrt(2 + A002193))/3).

A387297 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated triangular cupola (Johnson solid J_22).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 26 2025

Keywords

Comments

This is the dihedral angle between a triangular face and the hexagonal face.

Examples

			1.7261206622946734694269434030970502773414686910539...

Links

Crossrefs

Cf. other J_22 dihedral angles: A195698, A387294, A387295, A387296.
Cf. A344076 (J_22 volume), A344077 (J_22 surface area).
Cf. A010469.

Programs

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

Formula

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

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).

A387191 Decimal expansion of the second largest dihedral angle, in radians, in an elongated pentagonal rotunda (Johnson solid J_21).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 22 2025

Keywords

Comments

This is the dihedral angle between a square face and a pentagonal face.
Also one of the dihedral angles in Johnson solids J_40-J_43, J_72-J_75, J_77-J_79 and J_82.

Examples

			2.677945044588987122248387151818288482168632345...

Links

Crossrefs

Cf. other J_21 dihedral angles: A019669, A228824, A344075, A386530.
Cf. A384213 (J_21 volume), A179637 (J_21 surface area - 10).
Cf. A010476, A105199.

Programs

  • Mathematica
    First[RealDigits[Pi/2 + ArcTan[2], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J21", "DihedralAngles"]], 2], 10, 100]]

Formula

Equals Pi/2 + arctan(2) = A019669 + A105199.
Equals arccos(-2*sqrt(5)/5) = arccos(-A010476/5).

A386530 Decimal expansion of the largest dihedral angle, in radians, in an elongated pentagonal rotunda (Johnson solid J_21).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 22 2025

Keywords

Comments

This is the dihedral angle between a triangular face and a square face (at the edge where the prism and rotunda parts of the solid meet).
Also the analogous dihedral angle in Johnson solids J_40-J_43.

Examples

			2.9528821228062311686815089830968947118603985336982...

Links

Crossrefs

Cf. other J_21 dihedral angles: A019669, A228824, A344075, A387191.
Cf. A384213 (J_21 volume), A179637 (J_21 surface area - 10).
Cf. A002163.

Programs

  • Mathematica
    First[RealDigits[ArcCos[-Sqrt[2*(5 + Sqrt[5])/15]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J21", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(-sqrt(2*(5 + sqrt(5))/15)) = arccos(-sqrt(2*(5 + A002163)/15)).

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