A380863 -id:A380863 - cp's OEIS frontend

A380861 Decimal expansion of the smallest acute vertex angle, in radians, in a deltoidal hexecontahedron face.

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

Offset: 1

Paolo Xausa, Feb 06 2025

A deltoidal hexecontahedron face is a kite with one smallest acute angle (this constant), two largest acute angles (A380862) and one obtuse angle (A380863).

			1.1830367284200834147901361867998878650548206683684...

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

Cf. A002163, A379385, A379386, A379387, A379388, A379389, A380862, A380863.

First[RealDigits[ArcCos[(9*Sqrt[5] - 5)/40], 10, 100]]

Equals arccos((9*sqrt(5) - 5)/40) = arccos((9*A002163 - 5)/40).

Equals 2*Pi - 2*A380862 - A380863.

A380862 Decimal expansion of the largest acute angles, in radians, in a deltoidal hexecontahedron face.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Feb 06 2025

A deltoidal hexecontahedron face is a kite with one smallest acute angle (A380861), two largest acute angles (this constant) and one obtuse angle (A380863).

			1.517985377460215463602191357386072448171233382527...

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

Cf. A020762, A379385, A379386, A379387, A379388, A379389, A380861, A380863.

First[RealDigits[ArcCos[1/2 - 1/Sqrt[5]], 10, 100]]

Equals arccos(1/2 - 1/sqrt(5)) = arccos(1/2 - A020762).

Equals (2*Pi - A380861 - A380863)/2.

cp's OEIS Frontend

A380861 Decimal expansion of the smallest acute vertex angle, in radians, in a deltoidal hexecontahedron face.

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