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.

A384214 Decimal expansion of the volume of a gyroelongated square cupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 23 2025

Keywords

Comments

The gyroelongated square cupola is Johnson solid J_23.

Examples

			6.21076579203920003665822883345980731696010032091...

Links

Crossrefs

Cf. A384215 (surface area).
Cf. A002193, A010466, A179587, A179638, A384142.

Programs

  • Mathematica
    First[RealDigits[1 + Sqrt[8]/3 + 2/3*Sqrt[4 + Sqrt[8] + 2*Sqrt[146 + 103*Sqrt[2]]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J23", "Volume"], 10, 100]]

Formula

Equals 1 + (2/3)*sqrt(2) + (2/3)*sqrt(4 + 2*sqrt(2) + 2*sqrt(146 + 103*sqrt(2))) = 1 + A010466/3 + (2/3)*sqrt(4 + A010466 + 2*sqrt(146 + 103*A002193)).
Equals the largest real root of 6561*x^8 - 52488*x^7 + 113724*x^6 - 9720*x^5 - 1616922*x^4 + 396360*x^3 + 1537020*x^2 - 178632*x - 3391.

A179639 Decimal expansion of the volume of gyroelongated pentagonal pyramid with edge length 1.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2010

Keywords

Comments

Gyroelongated pentagonal pyramid: 11 vertices,25 edges,and 16 faces.

Examples

			1.88019215822908780282010679244089525495689855152098881326825313369561...

Links

Crossrefs

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A179554, A179587, A179588, A179589, A179590, A179591, A179592, A179593, A179637, A179638.

Programs

  • Mathematica
    RealDigits[N[(25+9*Sqrt[5])/24,200]]

Formula

Digits of (25+9*sqrt(5))/24.

A179640 Decimal expansion of the surface area of gyroelongated pentagonal pyramid with edge length 1.

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2010

Keywords

Comments

Gyroelongated pentagonal pyramid: 11 vertices, 25 edges, and 16 faces.

Examples

			8.21566792897225677348693575803563097544289387179912568441637087996861...

Links

Crossrefs

Cf. A001622, A010527, A102208, A179290, A179292, A179294, A179449, A179450, A179451, A179452, A179552, A179553, A179554, A179587, A179588, A179589, A179590, A179591, A179592, A179593, A179637, A179638, A179639.

Programs

  • Mathematica
    RealDigits[N[Sqrt[5/2*(70+Sqrt[5]+3*Sqrt[75+30*Sqrt[5]])]/2,200]]

Formula

Digits of sqrt(5/2*(70+sqrt(5)+3*sqrt(75+30*sqrt(5))))/2.

A387148 Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated square pyramid (Johnson solid J_10).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 19 2025

Keywords

Comments

This is the dihedral angle between a triangular face in the square pyramid part and a triangular face in the square antiprism part of the solid.
Also the analogous dihedral angle in a gyroelongated square bipyramid (Johnson solid J_17).

Examples

			2.76759950111674795948641922563774170695233176699...

Links

Crossrefs

Cf. other J_10 dihedral angles: A156546, A387149, A387150.
Cf. A179638 (J_10 volume), A374948 (J_10 surface area).
Cf. A002193, A011027.

Programs

  • Mathematica
    First[RealDigits[ArcCos[(1 - Sqrt[2] - 32^(1/4))/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J10", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos((1 - sqrt(2) - 2*2^(1/4))/3) = arccos((1 - A002193 - A011027)/3).

A387149 Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated square pyramid (Johnson solid J_10).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 19 2025

Keywords

Comments

This is the dihedral angle between adjacent triangular faces in the square antiprism part of the solid.
Also the analogous dihedral angle in a gyroelongated square bipyramid (Johnson solid J_17).

Examples

			2.2261954369024298095991888315497640747046712455090...

Links

Crossrefs

Cf. other J_10 dihedral angles: A156546, A387148, A387150.
Cf. A179638 (J_10 volume), A374948 (J_10 surface area).
Cf. A010466.

Programs

  • Mathematica
    First[RealDigits[ArcCos[(1 - Sqrt[8])/3], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J10", "DihedralAngles"]], 2], 10, 100]]

Formula

Equals arccos((1 - 2*sqrt(2))/3) = arccos((1 - A010466)/3).

A387150 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated square pyramid (Johnson solid J_10).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 19 2025

Keywords

Comments

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

Examples

			1.81228288299223868132256212312198395270891707198...

Links

Crossrefs

Cf. other J_10 dihedral angles: A156546, A387148, A387149.
Cf. A179638 (J_10 volume), A374948 (J_10 surface area).
Cf. A010466.

Programs

  • Mathematica
    First[RealDigits[ArcCos[-Sqrt[1 - Sqrt[8]/3]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J10", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(-sqrt(1 - 2*sqrt(2)/3)) = arccos(-sqrt(1 - A010466/3)).

A384142 Decimal expansion of the volume of a gyroelongated square bipyramid with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 22 2025

Keywords

Comments

The gyroelongated square bipyramid is Johnson solid J_17.

Examples

			1.428404502627748400527146549078867927980904164...

Links

Crossrefs

Cf. A010502 (surface area).
Cf. A002193, A010474, A179638.

Programs

  • Mathematica
    First[RealDigits[(Sqrt[2] + Sqrt[4 + Sqrt[18]])/3, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J17", "Volume"], 10, 100]]

Formula

Equals (sqrt(2) + sqrt(4 + 3*sqrt(2)))/3 = (A002193 + sqrt(4 + A010474))/3.
Equals the largest real root of 81*x^4 - 108*x^2 - 72*x-14.
Showing 1-7 of 7 results.

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