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

1,1

Comments

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

Links

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

Wikipedia, Pentagonal icositetrahedron.

Formula

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

Example

2.37904491483881068171953729116462006612803023...

Mathematica

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

Crossrefs

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

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

Sequence in context: A098863 A053960 A114056 * A168222 A323384 A349641

Adjacent sequences: A378824 A378825 A378826 * A378828 A378829 A378830

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 10 2024

Status

approved