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 1-6 of 6 results.

A384624 Decimal expansion of the volume of a pentagonal orthobicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 05 2025

Keywords

Comments

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

Examples

			4.6480906366663862618788982249750349805874911461487...

Links

Crossrefs

Cf. A384625 (surface area).
Cf. A010532, A384287.

Programs

  • Mathematica
    First[RealDigits[(5 + Sqrt[80])/3, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J30", "Volume"], 10, 100]]

Formula

Equals (5 + 4*sqrt(5))/3 = (5 + A010532)/3.
Equals the largest root of 9*x^2 - 30*x - 55.

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.

A384909 Decimal expansion of the volume of an elongated pentagonal orthobicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 12 2025

Keywords

Comments

The elongated pentagonal orthobicupola is Johnson solid J_38.
Also the volume of an elongated pentagonal gyrobicupola (Johnson solid J_39) with unit edge.

Examples

			12.342299479604519768304624665067309540604246504993...

Links

Crossrefs

Cf. A384625 (surface area - 10).
Cf. A002163, A010476, A384283, A384624, A384871.

Programs

  • Mathematica
    First[RealDigits[(10 + 8*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J38", "Volume"], 10, 100]]

Formula

Equals (10 + 8*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (10 + 8*A002163 + 15*sqrt(5 + A010476))/6.
Equals the largest root of 1296*x^4 - 8640*x^3 - 82440*x^2 - 109200*x + 76525.

A385857 Decimal expansion of the volume of a metabidiminished icosahedron with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 14 2025

Keywords

Comments

The metabidiminished icosahedron is Johnson solid J_62.

Examples

			1.5786893258332632321363912229104254118135394532...

Links

Crossrefs

Cf. A384625 (surface area + 10).
Cf. A010476, A102208, A179552, A386000, A386002.

Programs

  • Mathematica
    First[RealDigits[(5 + Sqrt[20])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J62", "Volume"], 10, 100]]

Formula

Equals (5 + 2*sqrt(5))/6 = (5 + A010476)/6.
Equals A102208 - 2*A179552.
Equals the largest root of 36*x^2 - 60*x + 5.

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.

A387189 Decimal expansion of the smallest dihedral angle, in radians, in a pentagonal bipyramid (Johnson solid J_13).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 21 2025

Keywords

Comments

This is the dihedral angle between triangular faces at the edge where the two pyramidal parts of the solid meet.
Also the dihedral angle between triangular faces in a pentagonal orthobicupola (Johnson solid J_30).

Examples

			1.3047162795687363719907812632876451487306158399...

Links

Crossrefs

Cf. A236367 (J_13 smallest dihedral angle).
Cf. other J_30 dihedral angles: A105199, A377995, A377996.
Cf. A179641 (J_13 volume), A120011 (J_13 surface area, divided by 10).
Cf. A384624 (J_30 volume), A384625 (J_30 surface area).
Cf. A010532, A386852.

Programs

  • Mathematica
    First[RealDigits[ArcCos[(Sqrt[80] - 5)/15], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J13", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos((4*sqrt(5) - 5)/15) = arccos((A010532 - 5)/15).
Equals 2*A386852.
Showing 1-6 of 6 results.

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