A380004 Decimal expansion of obtuse vertex angles, in radians, in a pentagonal hexecontahedron face.

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

Offset

1,1

Comments

A pentagonal hexecontahedron face is an irregular pentagon with one acute angle (A380003) and four (equal) obtuse angles (this constant).

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 smallest real root of 64*x^6 - 128*x^5 + 64*x^4 + 24*x^3 - 24*x^2 + 1.

Equals (3*Pi - A380003)/4.

Example

2.06187303432440735586609817608931599292105069088...

Mathematica

First[RealDigits[ArcCos[Root[64*#^6 - 128*#^5 + 64*#^4 + 24*#^3 - 24*#^2 + 1 &, 1]], 10, 100]]

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379890 (midradius), A379892 (dihedral angle), A380002 (long/short edge length ratio), A380003 (face acute angle).

Sequence in context: A347133 A317842 A021489 * A393079 A092158 A051831

Adjacent sequences: A380001 A380002 A380003 * A380005 A380006 A380007

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jan 12 2025

Status

approved