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 1-8 of 8 results.

A385258 Decimal expansion of the volume of a gyroelongated square bicupola with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jun 26 2025

Keywords

Comments

The gyroelongated square bicupola is Johnson solid J_45.

Examples

			8.1535748336212634025260213162662727026732149...

Links

Crossrefs

Cf. A385259 (surface area).
Cf. A002193, A010466, A179587, A384214, A384287, A385256.

Programs

  • Mathematica
    First[RealDigits[2/3*(3 + 2*# + Sqrt[2*(2 + # + Sqrt[146 + 103*#])]) & [Sqrt[2]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J45", "Volume"], 10, 100]]

Formula

Equals (2/3)*(3 + 2*sqrt(2) + sqrt(2*(2 + sqrt(2) + sqrt(146 + 103*sqrt(2))))) = (2/3)*(3 + A010466 + sqrt(2*(2 + A002193 + sqrt(146 + 103*A002193)))).
Equals the largest real root of 6561*x^8 - 104976*x^7 + 594864*x^6 - 1384128*x^5 - 552096*x^4 + 1569024*x^3 + 246528*x^2 - 119808*x + 4352.

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.

A387320 Decimal expansion of the largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 27 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 square bicupola (Johnson solid J_45).

Examples

			2.687150505637070622058237671034217872408094243788...

Links

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387321, A387322, A387323.
Cf. A384214 (J_23 volume), A384215 (J_23 surface area).
Cf. A385258 (J_45 volume), A385259 (J_45 surface area).
Cf. A002193.

Programs

  • Mathematica
    First[RealDigits[ArcCos[(1 - Sqrt[8 + Sqrt[32]])/3], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["J23", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos((1 - 2*sqrt(2 + sqrt(2)))/3) = arccos((1 - 2*sqrt(2 + A002193))/3).

A387321 Decimal expansion of the second largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 27 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 square bicupola (Johnson solid J_45).

Examples

			2.6412090003740395440214510528511358326798716782548...

Links

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387322, A387323.
Cf. A384214 (J_23 volume), A384215 (J_23 surface area).
Cf. A385258 (J_45 volume), A385259 (J_45 surface area).
Cf. A002193, A010487, A195696.

Programs

  • Mathematica
    First[RealDigits[ArcSec[Sqrt[3]] + ArcCos[-Sqrt[(7 + Sqrt[32] - 2*Sqrt[20 + 14*Sqrt[2]])/3]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J23", "DihedralAngles"]],2], 10, 100]]

Formula

Equals arcsec(sqrt(3)) + arccos(-sqrt((7 + 4*sqrt(2) - 2*sqrt(20 + 14*sqrt(2)))/3)) = A195696 + arccos(-sqrt((7 + A010487 - 2*sqrt(20 + 14*A002193))/3)).
Equals A195696 + A387323.

A387322 Decimal expansion of the fourth largest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 29 2025

Keywords

Comments

This is the dihedral angle between a triangular face and a square face at the edge where the antiprism and cupola parts of the solid meet.
Also the analogous dihedral angle in a gyroelongated square bicupola (Johnson solid J_45).

Examples

			2.4712905456469785754732547961552537994857493330886...

Links

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387321, A387323.
Cf. A384214 (J_23 volume), A384215 (J_23 surface area).
Cf. A385258 (J_45 volume), A385259 (J_45 surface area).
Cf. A003881, A002193, A010487.

Programs

  • Mathematica
    First[RealDigits[Pi/4 + ArcCos[-Sqrt[(7 + Sqrt[32] - 2*Sqrt[20 + 14*Sqrt[2]])/3]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J23", "DihedralAngles"]], 4], 10, 100]]

Formula

Equals Pi/4 + arccos(-sqrt((7 + 4*sqrt(2) - 2*sqrt(20 + 14*sqrt(2)))/3)) = A003881 + arccos(-sqrt((7 + A010487 - 2*sqrt(20 + 14*A002193))/3)).
Equals A003881 + A387323.

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.

A386696 Decimal expansion of the volume of a snub square antiprism with unit edges.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 31 2025

Keywords

Comments

The snub square antiprism is Johnson solid J_85.

Examples

			3.601222009733930312488413957294053408882603461...

Links

Crossrefs

Cf. A385259 (surface area + 8).
Cf. A386695.

Programs

  • Mathematica
    First[RealDigits[Root[531441*#^12 - 85726026*#^8 - 48347280*#^6 + 11588832*#^4 + 4759488*#^2 - 892448 &, 6], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J85", "Volume"], 10, 100]]

Formula

Equals the largest real root of 531441*x^12 - 85726026*x^8 - 48347280*x^6 + 11588832*x^4 + 4759488*x^2 - 892448.

A385694 Decimal expansion of the volume of a triaugmented hexagonal prism with unit edge.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 07 2025

Keywords

Comments

The triaugmented hexagonal prism is Johnson solid J_57.

Examples

			3.3051829925398634646920138743636575896990438184040...

Links

Crossrefs

Cf. A385259 (surface area + 7).
Cf. A010503, A104956, A385569, A385578.

Programs

  • Mathematica
    First[RealDigits[1/Sqrt[2] + 3*Sqrt[3]/2, 10, 100]]
First[RealDigits[PolyhedronData["J57", "Volume"], 10, 100]]

Formula

Equals 1/sqrt(2) + 3*sqrt(3)/2 = A010503 + A104956.
Equals the largest root of 16*x^4 - 232*x^2 + 625.
Showing 1-8 of 8 results.

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