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 1-9 of 9 results.

A385259 Decimal expansion of the surface area of a gyroelongated square bicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 26 2025

Keywords

Comments

The gyroelongated square bicupola is Johnson solid J_45.

Examples

			20.392304845413263761164678049035234201656831522862...

Links

Crossrefs

Cf. A385258 (volume).
Cf. A002194, A179588, A384215, A385257.

Programs

  • Mathematica
    First[RealDigits[10 + 6*Sqrt[3], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J45", "SurfaceArea"], 10, 100]]

Formula

Equals 10 + 6*sqrt(3) = 10 + 6*A002194.
Equals the largest root of x^2 - 20*x - 8.

A385256 Decimal expansion of the volume of a gyroelongated triangular bicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 24 2025

Keywords

Comments

The gyroelongated triangular bicupola is Johnson solid J_44.

Examples

			4.6945643929158936762142216512961490819695690656940...

Links

Crossrefs

Cf. A385257 (surface area).
Cf. A002193, A002193, A384143.

Programs

  • Mathematica
    First[RealDigits[Sqrt[2]*(5/3 + Sqrt[1 + Sqrt[3]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J44", "Volume"], 10, 100]]

Formula

Equals sqrt(2)*(5/3 + sqrt(1 + sqrt(3))) = A002193*(5/3 + sqrt(A090388)).
Equals the largest real root of 6561*x^8 - 198288*x^6 + 1506600*x^4 - 7125696*x^2 + 2704.

A385261 Decimal expansion of the surface area of a gyroelongated pentagonal bicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 27 2025

Keywords

Comments

The gyroelongated pentagonal bicupola is Johnson solid J_46.

Examples

			26.431335857944513546973871516071261950885787743598...

Links

Crossrefs

Cf. A385260 (volume).
Cf. A002163, A002194, A384284, A385257, A385259.

Programs

  • Mathematica
    First[RealDigits[(20 + 15*Sqrt[3] + Sqrt[25 + 10*Sqrt[5]])/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J46", "SurfaceArea"], 10, 100]]

Formula

Equals (20 + 15*sqrt(3) + sqrt(25 + 10*sqrt(5)))/2 = (20 + 15*A002194 + sqrt(25 + 10*A002163))/2.
Equals the largest root of x^8 - 80*x^7 + 2100*x^6 - 14000*x^5 - 174750*x^4 + 1390000*x^3 + 9603125*x^2 + 9937500*x - 6546875.

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).

A385263 Decimal expansion of the surface area of a gyroelongated pentagonal cupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 30 2025

Keywords

Comments

The gyroelongated pentagonal cupolarotunda is Johnson solid J_47.

Examples

			32.198786370350444777678239329896650406601165160912...

Links

Crossrefs

Cf. A385262 (volume).
Cf. A002163, A002194, A384284, A385257, A385259, A385261.

Programs

  • Mathematica
    First[RealDigits[5 + (35*Sqrt[3] + 7*Sqrt[25 + 10*Sqrt[5]])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J47", "SurfaceArea"], 10, 100]]

Formula

Equals 5 + (35*sqrt(3) + 7*sqrt(25 + 10*sqrt(5)))/4 = 5 + (35*A002194 + 7*sqrt(25 + 10*A002163))/4.
Equals the largest root of 256*x^8 - 10240*x^7 - 134400*x^6 + 7616000*x^5 - 756000*x^4 - 1373680000*x^3 + 2724312500*x^2 + 55840875000*x - 106054671875.

A385578 Decimal expansion of the volume of a parabiaugmented hexagonal prism with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 04 2025

Keywords

Comments

The parabiaugmented hexagonal prism is Johnson solid J_55.
Also the volume of a metabiaugmented hexagonal prism (Johnson solid J_56) with unit edge.

Examples

			3.0694807321443476232250657536620412432707651725...

Links

Crossrefs

Cf. A385257 (surface area + 2).
Cf. A002194, A010466, A104956, A131594, A385569.

Programs

  • Mathematica
    First[RealDigits[(Sqrt[8] + 9*Sqrt[3])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J55", "Volume"], 10, 100]]

Formula

Equals (2*sqrt(2) + 9*sqrt(3))/6 = (A010466 + 9*A002194)/6 = A131594 + A104956.
Equals the largest root of 1296*x^4 - 18072*x^2 + 55225.

A386752 Decimal expansion of the volume of a disphenocingulum with unit edges.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 01 2025

Keywords

Comments

The disphenocingulum is Johnson solid J_90.

Examples

			3.7776453418585752428818131132610964733952267025...

Links

Crossrefs

Cf. A385257 (surface area + 2).

Programs

  • Mathematica
    First[RealDigits[Root[1213025622610333925376*#^24 + 54451372392730545094656*#^22 - 796837093078664749252608*#^20 - 4133410366404688544268288*#^18 + 20902529024429842816303104*#^16 - 133907540390420673677230080*#^14 + 246234688242991598853881856*#^12 - 63327534106871321714442240*#^10 + 14389309497459555704164608*#^8 + 48042947402464500749392128*#^6 - 5891096640600351061013664*#^4 - 3212114716816853362953264*#^2 + 479556973248657693884401 &, 8], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J90", "Volume"], 10, 100]]

Formula

Equals the largest real root of 1213025622610333925376*x^24 + 54451372392730545094656*x^22 - 796837093078664749252608*x^20 - 4133410366404688544268288*x^18 + 20902529024429842816303104*x^16 - 133907540390420673677230080*x^14 + 246234688242991598853881856*x^12 - 63327534106871321714442240*x^10 + 14389309497459555704164608*x^8 + 48042947402464500749392128*x^6 - 5891096640600351061013664*x^4 - 3212114716816853362953264*x^2 + 479556973248657693884401.
Showing 1-9 of 9 results.

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