A377997 -id:A377997 - cp's OEIS frontend

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

Paolo Xausa, Jan 10 2025

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

			2.6734732271767846682790703348957917197870317502693...

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.

Cf. A379888 (surface area), A379889 (volume), A379890 (inradius), A379891 (midradius).
Cf. A377997 and A377998 (dihedral angles of a snub dodecahedron).
Cf. A377849.

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

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

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.

A377998 Decimal expansion of the dihedral angle, in radians, between triangular and pentagonal faces in a snub dodecahedron.

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Nov 15 2024

			2.669130633625756107707940935718208230518703745355...

Eric Weisstein's World of Mathematics, Snub Dodecahedron.
Wikipedia, Snub dodecahedron.

Cf. A001622, A377804, A377805, A377806, A377807, A377849, A377997.

First[RealDigits[Pi - ArcCos[Root[91125*#^12 - 668250*#^10 + 2006775*#^8 - 2735100*#^6 + 1768275*#^4 - 502410*#^2 + 43681&, 7]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["SnubDodecahedron", "DihedralAngles"]], 10, 100]]

Equals Pi - arccos(sqrt((12*phi - (4*phi + 8)*xi*(xi + 1) + 19)/15)), where phi = A001622 and xi = A377849.

Equals Pi - arccos(c), where c is the real root closest to 9/10 of 91125*x^12 - 668250*x^10 + 2006775*x^8 - 2735100*x^6 + 1768275*x^4 - 502410*x^2 + 43681.

cp's OEIS Frontend

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

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