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 1-3 of 3 results.

A387607 Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Sep 04 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 pentagonal rotunda, gyroelongated pentagonal bicupola, gyroelongated pentagonal cupolarotunda and gyroelongated pentagonal birotunda (Johnson solids J_25, J_46, J_47 and J_48, respectively).
Also the analogous dihedral angle in a decagonal antiprism.

Examples

			2.7783286661990213551074289190050780042508333364090...

Links

Crossrefs

Cf. other J_24 dihedral angles: A377995, A377996, A387608, A387609, A387610.
Cf. A384283 (J_24 volume), A384284 (J_24 surface area).
Cf. A384285 (J_25 volume), A384286 (J_25 surface area).
Cf. A385260 (J_46 volume), A385261 (J_46 surface area).
Cf. A385262 (J_47 volume), A385263 (J_47 surface area).
Cf. A385264 (J_48 volume), A385488 (J_48 surface area).
Cf. A010476.

Programs

  • Mathematica
    First[RealDigits[ArcCos[(1 - Sqrt[10 + Sqrt[20]])/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J24", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos((1 - sqrt(10 + 2*sqrt(5)))/3) = arccos((1 - sqrt(10 + A010476))/3).

A387608 Decimal expansion of the fourth largest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Sep 04 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 pentagonal bicupola and gyroelongated pentagonal cupolarotunda (Johnson solids J_46 and J_47, respectively).

Examples

			2.314725687375130081473793791474182971134043297238...

Links

Crossrefs

Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387609, A387610.
Cf. A384283 (J_24 volume), A384284 (J_24 surface area).
Cf. A385260 (J_46 volume), A385261 (J_46 surface area).
Cf. A385262 (J_47 volume), A385263 (J_47 surface area).
Cf. A002163, A002194, A010476, A386852.

Programs

  • Mathematica
    First[RealDigits[ArcSec[Sqrt[15 - 6*#]] + ArcCos[(Sqrt[5 + 2*#] - # - 1)/Sqrt[3]] & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J24", "DihedralAngles"]],4], 10, 100]]

Formula

Equals arccos(sqrt((5 + 2*sqrt(5))/15)) + arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = arccos(sqrt((5 + A010476)/15)) + arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).
Equals A386852 + A387610.

A387609 Decimal expansion of the fifth largest (second smallest) dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Sep 05 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 pentagonal bicupola and gyroelongated pentagonal cupolarotunda (Johnson solids J_46 and J_47, respectively).

Examples

			2.2159419064878071469869358899196289168037591999759...

Links

Crossrefs

Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387608, A387610.
Cf. A384283 (J_24 volume), A384284 (J_24 surface area).
Cf. A385260 (J_46 volume), A385261 (J_46 surface area).
Cf. A385262 (J_47 volume), A385263 (J_47 surface area).
Cf. A002163, A002194, A010476, A195693.

Programs

  • Mathematica
    First[RealDigits[ArcTan[2]/2 + ArcCos[(Sqrt[5 + Sqrt[20]] - Sqrt[5] - 1)/Sqrt[3]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J24", "DihedralAngles"]], 5], 10, 100]]

Formula

Equals arctan(2)/2 + arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = A195693 + arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).
Equals A195693 + A387610.
Showing 1-3 of 3 results.

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