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 1-5 of 5 results.

A378713 Decimal expansion of the volume of a disdyakis dodecahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Dec 07 2024

Keywords

Comments

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

Examples

			16.288919082923525038503122503619441045996797447357...

Links

Crossrefs

Cf. A378712 (surface area), A378714 (inradius), A378393 (midradius), A378715 (dihedral angle).
Cf. A377344 (volume of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length).
Cf. A002193.

Programs

  • Mathematica
    First[RealDigits[Sqrt[6582 + 4539*Sqrt[2]]/7, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["DisdyakisDodecahedron", "Volume"], 10, 100]]
  • PARI
    sqrt(3*(2194 + 1513*sqrt(2)))/7 \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals sqrt(3*(2194 + 1513*sqrt(2)))/7 = sqrt(6582 + 4539*A002193)/7.

A377343 Decimal expansion of the surface area of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Oct 26 2024

Keywords

Examples

			61.7551724393036681079496207885868453461497255502...

Links

Crossrefs

Cf. A377344 (volume), A377345 (circumradius), A377346 (midradius).
Cf. A343199 (analogous for a cuboctahedron).
Cf. A135611.

Programs

  • Mathematica
    First[RealDigits[12*(2 + Sqrt[2] + Sqrt[3]), 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedCuboctahedron", "SurfaceArea"], 10, 100]]

Formula

Equals 12*(2 + sqrt(2) + sqrt(3)) = 12*(2 + A135611).

A377345 Decimal expansion of the circumradius of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Oct 26 2024

Keywords

Examples

			2.3176109128927665137791474633402948053450518945...

Links

Crossrefs

Cf. A377343 (surface area), A377344 (volume), A377346 (midradius).
Cf. A010524.

Programs

  • Mathematica
    First[RealDigits[Sqrt[13 + 6*Sqrt[2]]/2, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedCuboctahedron", "Circumradius"], 10, 100]]

Formula

Equals sqrt(13 + 6*sqrt(2))/2 = sqrt(13 + A010524)/2.

A377346 Decimal expansion of the midradius of a truncated cuboctahedron (great rhombicuboctahedron) with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Oct 26 2024

Keywords

Examples

			2.26303343845371462359202580343253714222906720265...

Links

Crossrefs

Cf. A377343 (surface area), A377344 (volume), A377345 (circumradius).
Cf. A010527 (analogous for a cuboctahedron).
Cf. A010524, A230981.

Programs

  • Mathematica
    First[RealDigits[Sqrt[3 + 3/Sqrt[2]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedCuboctahedron", "Midradius"], 10, 100]]

Formula

Equals sqrt(12 + 6*sqrt(2))/2 = sqrt(12 + A010524)/2 = sqrt(3 + 3/sqrt(2)) = sqrt(3 + A230981).

A381689 Decimal expansion of the isoperimetric quotient of a truncated cuboctahedron (great rhombicuboctahedron).

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Mar 06 2025

Keywords

Comments

For the definition of isoperimetric quotient of a solid, references and links, see A381684.

Examples

			0.8390038051045342803688923433479361567507803475...

Links

Crossrefs

Cf. A377343 (surface area), A377344 (volume).
Cf. A002193, A002194, A010549, A019679, A381684.

Programs

  • Mathematica
    First[RealDigits[Pi/12*(11 + Sqrt[98])^2/(2 + Sqrt[2] + Sqrt[3])^3, 10, 100]]

Formula

Equals 36*Pi*A377344^2/(A377343^3).
Equals (Pi/12)*(11 + 7*sqrt(2))^2/((2 + sqrt(2) + sqrt(3))^3) = A019679*(11 + A010549)^2/((2 + A002193 + A002194)^3).
Showing 1-5 of 5 results.

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