A380796 Decimal expansion of the largest acute vertex angle, in radians, in a pentakis dodecahedron face.

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

Offset: 1

Author

Paolo Xausa, Feb 04 2025

Keywords

• nonn
• cons
• easy

Comments

A pentakis dodecahedron face is an acute isoscele triangle with the smallest angles being A380795 and the largest angle being this constant.

Examples

			1.1976226087563797890813284298421039858218935910...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.
• Wikipedia, Pentakis dodecahedron.

Crossrefs

Cf. A001622, A379132, A379133, A379135, A379136, A380795.

Programs

Mathematica

First[RealDigits[ArcCos[(9*GoldenRatio - 8)/18], 10, 100]]

Formula

Equals arccos((9*A001622 - 8)/18).

Equals Pi - 2*A380795.