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

1,1

Comments

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

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.

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.

Example

2.6734732271767846682790703348957917197870317502693...

Mathematica

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

Prog

(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

Crossrefs

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

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

Cf. A377849.

Sequence in context: A020771 A242113 A261804 * A021378 A329246 A201891

Adjacent sequences: A379889 A379890 A379891 * A379893 A379894 A379895

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jan 10 2025

Status

approved