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 1-10 of 12 results. Next

A384283 Decimal expansion of the volume of a gyroelongated pentagonal cupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 26 2025

Keywords

Comments

The gyroelongated pentagonal cupola is Johnson solid J_24.

Examples

			9.07333319388018799314998398101816272215313393060...

Links

Crossrefs

Cf. A384284 (surface area).
Cf. A002163, A010532, A179590, A179639, A179641, A384138, A384140, A384144, A384213.

Programs

  • Mathematica
    First[RealDigits[(5 + Sqrt[80] + 5*Sqrt[2*(Sqrt[650 + 290*Sqrt[5]] - Sqrt[5] - 1)])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J24", "Volume"], 10, 100]]
  • PARI
    (5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 \\ Charles R Greathouse IV, Aug 19 2025

Formula

Equals (5 + 4*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (5 + A010532 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.
Equals the largest real root of 1679616*x^8 - 11197440*x^7 + 27060480*x^6 + 35769600*x^5 - 4456749600*x^4 - 10714248000*x^3 + 3828402000*x^2 + 13859430000*x + 5340175625.

A384625 Decimal expansion of the surface area of a pentagonal orthobicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 05 2025

Keywords

Comments

The pentagonal orthobicupola is Johnson solid J_30.
Also the surface area of a pentagonal gyrobicupola (Johnson solid J_31) with unit edge.

Examples

			17.771081820100127079336639808541900116171761474546...

Links

Crossrefs

Cf. A384624 (volume).
Cf. A002163, A384284, A384286, A384872.

Programs

  • Mathematica
    First[RealDigits[10 + Sqrt[5*(10 + Sqrt[5] + Sqrt[75 + 30*Sqrt[5]])/2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J30", "SurfaceArea"], 10, 100]]

Formula

Equals 10 + sqrt(5*(10 + sqrt(5) + sqrt(75 + 30*sqrt(5)))/2) = 10 + sqrt(5*(10 + A002163 + sqrt(75 + 30*A002163))/2).
Equals the largest root of x^8 - 80*x^7 + 2700*x^6 - 50000*x^5 + 552750*x^4 - 3710000*x^3 + 14628125*x^2 - 30562500*x + 25328125.

A384286 Decimal expansion of the surface area of a gyroelongated pentagonal rotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 30 2025

Keywords

Comments

The gyroelongated pentagonal rotunda is Johnson solid J_25.

Examples

			31.00745430323851474443564586571797490853203978248...

Links

Crossrefs

Cf. A384285 (volume).
Cf. A002163, A002194, A179553, A179591, A179640, A384141, A384284.

Programs

  • Mathematica
    First[RealDigits[(15*Sqrt[3] + Sqrt[650 + 290*Sqrt[5]])/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J25", "SurfaceArea"], 10, 100]]

Formula

Equals (15*sqrt(3) + sqrt(650 + 290*sqrt(5)))/2 = (15*A002194 + sqrt(650 + 290*A002163))/2.
Equals the largest root of 256*x^8 - 339200*x^6 + 98924000*x^4 - 9264250000*x^2 + 176295015625.

A384872 Decimal expansion of the surface area of a pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 11 2025

Keywords

Comments

The pentagonal orthocupolarotunda is Johnson solid J_32.
Also the surface area of a pentagonal gyrocupolarotunda (Johnson solid J_33) with unit edge.

Examples

			23.538532332506058310041007622367288571887138891860...

Links

Crossrefs

Cf. A384871 (volume).
Cf. A002163, A002194, A384284, A384286, A384625.

Programs

  • Mathematica
    First[RealDigits[5 + 15/4*Sqrt[3] + 7/4*Sqrt[25 + 10*Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J32", "SurfaceArea"], 10, 100]]

Formula

Equals 5 + (15/4)*sqrt(3) + (7/4)*sqrt(25 + 10*sqrt(5)) = 5 + (15/4)*A002194 + (7/4)*sqrt(25 + 10*A002163).
Equals the largest root of 256*x^8 - 10240*x^7 + 57600*x^6 + 1856000*x^5 - 21756000*x^4 + 6320000*x^3 + 484812500*x^2 - 364125000*x - 342171875.

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.

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.

A384911 Decimal expansion of the surface area of an elongated pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 13 2025

Keywords

Comments

The elongated pentagonal orthocupolarotunda is Johnson solid J_40.
Also the surface area of an elongated pentagonal gyrocupolarotunda (Johnson solid J_41) with unit edge.

Examples

			33.538532332506058310041007622367288571887138891860...

Links

Crossrefs

Cf. A384910 (volume).
Cf. A002163, A384284, A384286, A384625.
Apart from the leading digit the same as A384872.

Programs

  • Mathematica
    First[RealDigits[(60 + Sqrt[10*(190 + 49*Sqrt[5] + 21*Sqrt[75 + 30*Sqrt[5]])])/4, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J40", "SurfaceArea"], 10, 100]]

Formula

Equals (60 + sqrt(10*(190 + 49*sqrt(5) + 21*sqrt(75 + 30*sqrt(5)))))/4 = (60 + sqrt(10*(190 + 49*A002163 + 21*sqrt(75 + 30*A002163))))/4.
Equals the largest root of 256*x^8 - 30720*x^7 + 1491200*x^6 - 37440000*x^5 + 509444000*x^4 - 3437040000*x^3 + 5993612500*x^2 + 44939625000*x - 172099671875.

A385488 Decimal expansion of the surface area of a gyroelongated pentagonal birotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 30 2025

Keywords

Comments

The gyroelongated pentagonal birotunda is Johnson solid J_48.

Examples

			37.966236882756376008382607143722038862316542578226...

Links

Crossrefs

Cf. A385264 (volume).
Cf. A002163, A002194, A384284, A385261, A385263.

Programs

  • Mathematica
    First[RealDigits[10*Sqrt[3] + 3*Sqrt[25 + 10*Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J48", "SurfaceArea"], 10, 100]]

Formula

Equals 10*sqrt(3) + 3*sqrt(25 + 10*sqrt(5)) = 10*A002194 + 3*sqrt(25 + 10*A002163).
Equals the largest root of x^8 - 2100*x^6 + 1032750*x^4 - 121162500*x^2 + 1216265625.

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.
Showing 1-10 of 12 results. Next

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