A379892 Decimal expansion of the dihedral angle, in radians, between any two adjacent faces in a pentagonal hexecontahedron.

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

Offset: 1

Author

Paolo Xausa, Jan 10 2025

Keywords

• nonn
• cons
• easy

Comments

The pentagonal hexecontahedron is the dual polyhedron of the snub dodecahedron.

Examples

			2.6734732271767846682790703348957917197870317502693...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pentagonal Hexecontahedron.
• Wikipedia, Pentagonal hexecontahedron.
• Index entries for transcendental numbers.

Crossrefs

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379891 (midradius).

Cf. A377997 and A377998 (dihedral angles of a snub dodecahedron).

Cf. A377849.

Programs

Mathematica

First[RealDigits[ArcCos[#/(# - 2)] & [Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1]], 10, 100]] (* or *)
First[RealDigits[First[PolyhedronData["PentagonalHexecontahedron", "DihedralAngles"]], 10, 100]]

PARI

acos(polrootsreal(209*x^6 - 94*x^5 - 137*x^4 + 100*x^3 - 9*x^2 - 6*x + 1)[1]) \\ Charles R Greathouse IV, Feb 10 2025

Formula

Equals arccos(A377849/(A377849 - 2)).

Equals arccos(c), where c is the smallest real root of 209*x^6 - 94*x^5 - 137*x^4 + 100*x^3 - 9*x^2 - 6*x + 1.