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 1-7 of 7 results.

A378715 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a disdyakis dodecahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 07 2024

Keywords

Comments

The disdyakis dodecahedron is the dual polyhedron of the truncated cuboctahedron (great rhombicuboctahedron).

Examples

			2.7066946454792287856258644383068280456984454555717...

Links

Crossrefs

Cf. A378712 (surface area), A378713 (volume), A378714 (inradius), A378393 (midradius).
Cf. A177870, A195698 and A195702 (dihedral angles of a truncated cuboctahedron (great rhombicuboctahedron)).
Cf. A002193.

Programs

  • Mathematica
    First[RealDigits[ArcCos[-(71 + 12*Sqrt[2])/97], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DisdyakisDodecahedron", "DihedralAngles"]], 10, 100]]

Formula

Equals arccos(-(71 + 12*sqrt(2))/97) = arccos(-(71 + 12*A002193)/97).

A378394 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a deltoidal icositetrahedron.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 30 2024

Keywords

Comments

The deltoidal icositetrahedron is the dual polyhedron of the (small) rhombicuboctahedron.

Examples

			2.410613141653407606153665785465949185980362906...

Links

Crossrefs

Cf. A378390 (surface area), A378391 (volume), A378392 (inradius), A378393 (midradius).
Cf. A177870 and A195702 (dihedral angles of a (small) rhombicuboctahedron).

Programs

  • Mathematica
    First[RealDigits[ArcSec[Sqrt[32] - 7], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["DeltoidalIcositetrahedron", "DihedralAngles"]], 10, 100]]
  • PARI
    acos(-(4*sqrt(2) + 7)/17) \\ Charles R Greathouse IV, Feb 11 2025

Formula

Equals arcsec(4*sqrt(2) - 7) = arcsec(A010487 - 7).
Equals arccos(-(4*sqrt(2) + 7)/17) = arccos(-(A010487 + 7)/17).

A195701 Decimal expansion of arctan(sqrt(2/3)).

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Sep 23 2011

Keywords

Examples

			arctan(sqrt(2/3)) = 0.68471920300...

Links

Crossrefs

Cf. A195695, A195695, A195702.

Programs

  • Magma
    [Arctan(Sqrt(2/3))]; // G. C. Greubel, Nov 18 2017
  • Mathematica
    r = Sqrt[2/3];
N[ArcSin[r], 100]
RealDigits[%]  (* A195696 *)
N[ArcCos[r], 100]
RealDigits[%]  (* A195695 *)
N[ArcTan[r], 100]
RealDigits[%]  (* A195701 *)
N[ArcCos[-r], 100]
RealDigits[%]  (* A195702 *)
  • PARI
    atan(sqrt(2/3)) \\ G. C. Greubel, Nov 18 2017

Formula

Equals arcsin(sqrt(2/5)) = arccos(sqrt(3/5)). - Amiram Eldar, Jul 10 2023

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.

A387323 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated square cupola (Johnson solid J_23).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Aug 29 2025

Keywords

Comments

This is the dihedral angle between a triangular face and the octagonal face.

Examples

			1.6858923822495302658575939503353780784364569832448...

Links

Crossrefs

Cf. other J_23 dihedral angles: A177870, A195702, A387320, A387321, A387322.
Cf. A384214 (J_23 volume), A384215 (J_23 surface area).
Cf. A002193, A003881, A010487, A195696.

Programs

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

Formula

Equals arccos(-sqrt((7 + 4*sqrt(2) - 2*sqrt(20 + 14*sqrt(2)))/3)) = arccos(-sqrt((7 + A010487 - 2*sqrt(20 + 14*A002193))/3)).
Equals A387321 - A195696 = A387322 - A003881.
Showing 1-7 of 7 results.

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