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.

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.

A384871 Decimal expansion of the volume of a pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 11 2025

Keywords

Comments

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

Examples

			9.2418082864578952008524451431901588238346215825240...

Links

Crossrefs

Cf. A384872 (surface area).
Cf. A002163, A384144, A384283, A384285, A384624.

Programs

  • Mathematica
    First[RealDigits[5*(11 + 5*Sqrt[5])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J32", "Volume"], 10, 100]]

Formula

Equals (5/12)*(11 + 5*sqrt(5)) = (5/12)*(11 + 5*A002163).
Equals the largest root of 36*x^2 - 330*x - 25.

A384910 Decimal expansion of the volume of an elongated pentagonal orthocupolarotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 13 2025

Keywords

Comments

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

Examples

			16.936017129396028707278171583282433383851376941...

Links

Crossrefs

Cf. A384911 (surface area).
Cf. A002163, A010476, A384283, A384285, A384624, A384871, A384909.

Programs

  • Mathematica
    First[RealDigits[5/12*(11 + 5*Sqrt[5] + 6*Sqrt[5 + Sqrt[20]]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J40", "Volume"], 10, 100]]

Formula

Equals (5/12)*(11 + 5*sqrt(5) + 6*sqrt(5 + 2*sqrt(5))) = (5/12)*(11 + 5*A002163 + 6*sqrt(5 + A010476)).
Equals the largest root of 1296*x^4 - 23760*x^3 + 26100*x^2 + 84000*x - 111875.

A384952 Decimal expansion of the volume of an elongated pentagonal orthobirotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 20 2025

Keywords

Comments

The elongated pentagonal orthobirotunda is Johnson solid J_42.
Also the volume of an elongated pentagonal gyrobirotunda (Johnson solid J_43) with unit edge.

Examples

			21.52973477918753764625171850149755722709850737774...

Links

Crossrefs

Cf. A179451 (surface area - 10), A344149 (surface area + 20).
Cf. A002163, A010476, A384283, A384285, A384624, A384871, A384909, A384910.

Programs

  • Mathematica
    First[RealDigits[(45 + 17*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J42", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (45 + 17*A002163 + 15*sqrt(5 + A010476))/6.
Equals the largest root of 1296*x^4 - 38880*x^3 + 252360*x^2 - 329400*x - 332975.

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).

A387610 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated pentagonal cupola (Johnson solid J_24).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Sep 05 2025

Keywords

Comments

This is the dihedral angle between a triangular face and the decagonal face.
Also the analogous dihedral angle in a gyroelongated pentagonal rotunda (Johnson solid J_25).
Also the analogous dihedral angle in a decagonal antiprism.

Examples

			1.662367547590761895478403159830360396768735377275...

Links

Crossrefs

Cf. other J_24 dihedral angles: A377995, A377996, A387607, A387608, A387609.
Cf. A384283 (J_24 volume), A384284 (J_24 surface area).
Cf. A384285 (J_25 volume), A384286 (J_25 surface area).
Cf. A002163, A002194, A010476, A195693, A386852.

Programs

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

Formula

Equals arccos((sqrt(5 + 2*sqrt(5)) - sqrt(5) - 1)/sqrt(3)) = arccos((sqrt(5 + A010476) - A002163 - 1)/A002194).
Equals A387608 - A386852.
Equals A387609 - A195693.
Showing 1-6 of 6 results.

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