A391146 Decimal expansion of the second smallest dihedral angle, in radians, in a disphenocingulum (Johnson solid J_90).

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

Offset

1,1

Links

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

Polytope Wiki, Disphenocingulum.

Wikipedia, Disphenocingulum.

Formula

Equals arccos(c), where c = -0.569307... is the largest negative real root of 531441*x^12 + 17714700*x^11 + 194743602*x^10 + 814167612*x^9 + 1478160495*x^8 + 1155453336*x^7 - 96884100*x^6 - 1588339368*x^5 - 2042658081*x^4 - 706449060*x^3 + 612044658*x^2 + 580836204*x + 135375265.

Example

2.176459066501222579898433924084539147055398826233...

Mathematica

First[RealDigits[ArcCos[Root[531441*#^12 + 17714700*#^11 + 194743602*#^10 + 814167612*#^9 + 1478160495*#^8 + 1155453336*#^7 - 96884100*#^6 - 1588339368*#^5 - 2042658081*#^4 - 706449060*#^3 + 612044658*#^2 + 580836204*# + 135375265 &, 6]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J90", "DihedralAngles"]], 2], 10, 100]]

Crossrefs

Cf. other J_90 dihedral angles: A391145, A391147, A391148, A391149, A391150, A391151.

Cf. A386752 (J_90 volume), A385257 (J_90 surface area + 2).

Sequence in context: A248950 A329058 A078301 * A160201 A204912 A178049

Adjacent sequences: A391143 A391144 A391145 * A391147 A391148 A391149

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 07 2025

Status

approved