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

0,1

Comments

A pentakis dodecahedron face is an acute isoscele triangle with the smallest angles being this constant and the largest angle being A380796.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Pentakis Dodecahedron.

Wikipedia, Pentakis dodecahedron.

Formula

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

Equals (Pi - A380796)/2.

Example

0.97198502241670672469065747671869944918763790417527...

Mathematica

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

Crossrefs

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

Sequence in context: A254249 A298752 A154396 * A069611 A083995 A195357

Adjacent sequences: A380792 A380793 A380794 * A380796 A380797 A380798

Keyword

nonn,cons,easy,new

Author

Paolo Xausa, Feb 04 2025

Status

approved