A380003 Decimal expansion of acute vertex angle, in radians, in a pentagonal hexecontahedron face.

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

Offset

1,3

Comments

A pentagonal hexecontahedron face is an irregular pentagon with one acute angle (this constant) and four (equal) obtuse angles (A380004).

Links

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

Eric Weisstein's World of Mathematics, Pentagonal Hexecontahedron.

Wikipedia, Pentagonal hexecontahedron.

Formula

Equals arccos(c), where c is the largest real root of 64*x^6 - 384*x^5 + 384*x^4 + 888*x^3 + 168*x^2 - 128*x - 31.

Equals 3*Pi - 4*A380004.

Example

1.1772858234717502919235374454812446809073054345981...

Mathematica

First[RealDigits[ArcCos[Root[64*#^6 - 384*#^5 + 384*#^4 + 888*#^3 + 168*#^2 - 128*# - 31 &, 4]], 10, 100]]

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379890 (midradius), A379892 (dihedral angle), A380002 (long/short edge length ratio), A380004 (face obtuse angles).

Sequence in context: A303658 A169812 A195907 * A126584 A318302 A266271

Adjacent sequences: A380000 A380001 A380002 * A380004 A380007 A380014

Keyword

nonn,cons,easy,new

Author

Paolo Xausa, Jan 12 2025

Status

approved