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A389307
Decimal expansion of the second smallest dihedral angle, in radians, in a pentagonal orthocupolarotunda (Johnson solid J_32).
1
1, 9, 3, 5, 6, 6, 0, 1, 5, 4, 9, 0, 8, 3, 7, 9, 8, 0, 0, 9, 5, 8, 7, 2, 0, 0, 2, 1, 5, 4, 6, 4, 1, 1, 7, 8, 9, 7, 9, 6, 8, 3, 7, 6, 5, 6, 7, 1, 1, 4, 0, 9, 7, 5, 5, 8, 4, 1, 9, 4, 7, 0, 4, 1, 8, 8, 4, 8, 1, 7, 6, 5, 2, 9, 7, 6, 4, 8, 8, 0, 6, 8, 7, 1, 1, 7, 5, 9, 1, 1
OFFSET
1,2
COMMENTS
This is the dihedral angle between a triangular face and a square face at the edge where the cupola and rotunda parts of the solid meet.
Also a dihedral angle in a bilunabirotunda and triangular hebesphenorotunda (Johnson solids J_91 and J_92, respectively).
FORMULA
Equals arccos((sqrt(3) - sqrt(15))/6) = arccos((A002194 - A010472)/6).
EXAMPLE
1.9356601549083798009587200215464117897968376567114...
MATHEMATICA
First[RealDigits[ArcCos[(Sqrt[3] - Sqrt[15])/6], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J32", "DihedralAngles"]], 2], 10, 100]]
CROSSREFS
Cf. other J_32 dihedral angles: A344075, A377995, A377996, A389109.
Cf. A384871 (J_32 volume), A384872 (J_32 surface area).
Sequence in context: A371857 A371604 A145924 * A324995 A200007 A153618
KEYWORD
nonn,cons,easy
AUTHOR
Paolo Xausa, Sep 29 2025
STATUS
approved