A377970 -id:A377970 - cp's OEIS frontend

A378827 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentagonal icositetrahedron.

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

Offset: 1

Paolo Xausa, Dec 10 2024

The pentagonal icositetrahedron is the dual polyhedron of the snub cube.

			2.37904491483881068171953729116462006612803023...

Paolo Xausa, Table of n, a(n) for n = 1..10000
Wikipedia, Pentagonal icositetrahedron.

Cf. A378823 (surface area), A378824 (volume), A378825 (inradius), A378826 (midradius).

Cf. A377969 and A377970 (dihedral angles of a snub cube).

First[RealDigits[ArcCos[Root[7*#^3 - #^2 - 3*# + 1 &, 1]], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["PentagonalIcositetrahedron", "DihedralAngles"]], 10, 100]]

Equals arccos(c), where c is the real root of 7*x^3 - x^2 - 3*x + 1.

A377969 Decimal expansion of the dihedral angle, in radians, between triangular faces in a snub cube.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Nov 13 2024

			2.674448083535228681556740855858728640985224997062...

Eric Weisstein's World of Mathematics, Snub Cube.

Cf. A058265, A377602, A377603, A377604, A377605, A377970.

First[RealDigits[Pi - ArcCos[Root[27*#^3 + 9*#^2 - 15*# - 13 &, 1]], 10, 100]] (* or *)
First[RealDigits[Max[PolyhedronData["SnubCube", "DihedralAngles"]], 10, 100]]

Equals 2*arcsec(sqrt(12*A377604^2 - 3)).
Equals Pi - arccos((2*A058265 - 1)/3).
Equals Pi - arccos(c), where c is the real root of 27*x^3 + 9*x^2 - 15*x - 13.

cp's OEIS Frontend

A378827 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentagonal icositetrahedron.

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