A380736 Decimal expansion of the smallest vertex angle, in radians, in a disdyakis dodecahedron face.

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

Offset

0,1

Comments

A disdyakis dodecahedron face is a scalene triangle with three acute angles.

Links

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

Wikipedia, Disdyakis dodecahedron.

Formula

Equals arccos(1/12 + sqrt(2)/2) = arccos(1/12 + A010503).

Equals Pi - A380737 - A380738.

Example

0.6592691539262158395617269590815416456187802510390...

Mathematica

First[RealDigits[ArcCos[1/12 + Sqrt[2]/2], 10, 100]]

Crossrefs

Cf. A380737 (face medium angle), A380738 (face largest angle).

Cf. A010503, A378393, A378712, A378713, A378714, A378715, A380734, A380735.

Sequence in context: A011284 A196760 A199949 * A165227 A242761 A200477

Adjacent sequences: A380733 A380734 A380735 * A380737 A380738 A380739

Keyword

nonn,cons,easy,new

Author

Paolo Xausa, Feb 01 2025

Status

approved