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.

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.

A384285 Decimal expansion of the volume of a gyroelongated pentagonal rotunda with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, May 29 2025

Keywords

Comments

The gyroelongated pentagonal rotunda is Johnson solid J_25.

Examples

			13.667050843671696932123530899233286565400264...

Links

Crossrefs

Cf. A384286 (surface area).
Cf. A002163, A179590, A179639, A179641, A384138, A384140, A384144, A384213, A384283.

Programs

  • Mathematica
    First[RealDigits[(45 + 17*# + 10*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/12 & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J25", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 10*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/12 = (45 + 17*A002163 + 10*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/12.
Equals the largest real root of 1679616*x^8 - 50388480*x^7 + 603262080*x^6 - 3520972800*x^5 + 5215460400*x^4 + 4128624000*x^3 - 8894943000*x^2 + 3881385000*x - 424924375.

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.

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.

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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