A378388 -id:A378388 - cp's OEIS frontend

A378389 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a tetrakis hexahedron.

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

Offset: 1

Paolo Xausa, Nov 27 2024

The tetrakis hexahedron is the dual polyhedron of the truncated octahedron.

			2.498091544796508851659834154562180246155658808...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Tetrakis hexahedron.

Cf. A378388 (surface area), A374359 (volume - 1), A010532 (inradius*10), A179587 (midradius + 1).

Cf. A156546 and A195698 (dihedral angles of a truncated octahedron), A195729.

First[RealDigits[ArcCos[-4/5], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["TetrakisHexahedron", "DihedralAngles"]], 10, 100]]

Equals arccos(-4/5).

Equals 2*A195729. - Amiram Eldar, Nov 27 2024

A382004 Decimal expansion of the isoperimetric quotient of a tetrakis hexahedron.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Mar 17 2025

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

			0.84297776772488716717876495718458737593598110244806...

Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers

Cf. A378388 (surface area), A374359 (volume - 1).

Cf. A000796, A002163, A381684.

First[RealDigits[3*Pi/5/Sqrt[5], 10, 100]]

Equals 36*Pi*(A374359 + 1)^2/(A378388^3).

Equals 3*Pi/(5*sqrt(5)) = (3/5)*A000796/A002163.

cp's OEIS Frontend

A378389 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a tetrakis hexahedron.

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