A380795 Decimal expansion of the smallest acute vertex angles, in radians, in a pentakis dodecahedron face.

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

Offset: 0

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 this constant and the largest angle being A380796.

Examples

			0.97198502241670672469065747671869944918763790417527...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.
• Wikipedia, Pentakis dodecahedron.

Crossrefs

Cf. A001622, A379132, A379133, A379135, A379136, A380796.

Programs

Mathematica

First[RealDigits[ArcCos[(5 - GoldenRatio)/6], 10, 100]]

Formula

Equals arccos((5 - A001622)/6).

Equals (Pi - A380796)/2.