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 1-3 of 3 results.

A378351 Decimal expansion of the surface area of a (small) triakis octahedron with unit shorter edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Nov 23 2024

Keywords

Comments

The (small) triakis octahedron is the dual polyhedron of the truncated cube.

Examples

			10.672941873983546705150008922490160564590104237715...

Links

Crossrefs

Cf. A378352 (volume), A378353 (inradius), A201488 (midradius), A378354 (dihedral angle).
Cf. A377298 (surface area of a truncated cube with unit edge).
Cf. A010487.

Programs

  • Mathematica
    First[RealDigits[3*Sqrt[7 + Sqrt[32]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TriakisOctahedron", "SurfaceArea"], 10, 100]]

Formula

Equals 3*sqrt(7 + 4*sqrt(2)) = 3*sqrt(7 + A010487).

A377299 Decimal expansion of the volume of a truncated cube with unit edge length.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Oct 25 2024

Keywords

Examples

			13.599663291074443561074547379645257699991802085...

Links

Crossrefs

Cf. A377298 (surface area), A294968 (circumradius), A010503 (midradius - 1), A377296 (Dehn invariant, negated).
Cf. A131594.

Programs

  • Mathematica
    First[RealDigits[7 + 14*Sqrt[2]/3, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedCube", "Volume"], 10, 100]]

Formula

Equals 7 + (14/3)*sqrt(2) = 7 + 14*A131594.

A381686 Decimal expansion of the isoperimetric quotient of a truncated cube.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Mar 04 2025

Keywords

Comments

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

Examples

			0.61302821107928032110240558144714079708976169223933...

Links

Crossrefs

Cf. A377298 (surface area), A377299 (volume).
Cf. A000796, A002194, A010524, A156164, A381684.

Programs

  • Mathematica
    First[RealDigits[49*Pi*(17 + 12*Sqrt[2])/(2*(6 + 6*Sqrt[2] + Sqrt[3])^3), 10, 100]]

Formula

Equals 36*Pi*A377299^2/(A377298^3).
Equals 49*Pi*(17 + 12*sqrt(2))/(2*(6 + 6*sqrt(2) + sqrt(3))^3) = 49*A000796*A156164/(2*(6 + A010524 + A002194)^3).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.