A390631 Decimal expansion of the second smallest dihedral angle, in radians, in a sphenomegacorona (Johnson solid J_88).

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

Offset

1,2

Links

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

Polytope Wiki, Sphenomegacorona.

Wikipedia, Sphenomegacorona.

Formula

Equals arccos(c), where c = 0.0570965... is the smallest positive real root of 474590099025*x^16 + 8330401447920*x^15 + 38493602358264*x^14 + 28727379125712*x^13 - 158544634097700*x^12 - 314283025881360*x^11 + 52863983353800*x^10 + 636092644840272*x^9 + 559684281186342*x^8 + 10826887562064*x^7 - 176108527200312*x^6 - 35636233431312*x^5 + 1271297267676*x^4 - 38666797214256*x^3 - 27672129676296*x^2 - 4570448236560*x + 358379590225.

Example

1.513668735550279303639160376519664172036217037287...

Mathematica

First[RealDigits[ArcCos[Root[474590099025*#^16 + 8330401447920*#^15 + 38493602358264*#^14 + 28727379125712*#^13 - 158544634097700*#^12 - 314283025881360*#^11 + 52863983353800*#^10 + 636092644840272*#^9 + 559684281186342*#^8 + 10826887562064*#^7 - 176108527200312*#^6 - 35636233431312*#^5 + 1271297267676*#^4 - 38666797214256*#^3 - 27672129676296*#^2 - 4570448236560*# + 358379590225 &, 7]], 10, 100]] (* or *)
First[RealDigits[RankedMin[Union[PolyhedronData["J88", "DihedralAngles"]], 2], 10, 100]]

Crossrefs

Cf. other J_88 dihedral angles: A390630, A390632, A390633, A390634, A390635, A390636, A390637, A390638.

Cf. A334114 (J_88 volume), A010502 (J_88 surface area - 2).

Sequence in context: A053544 A388074 A174879 * A327965 A094136 A051996

Adjacent sequences: A390628 A390629 A390630 * A390632 A390633 A390634

Keyword

nonn,cons,easy

Author

Paolo Xausa, Nov 19 2025

Status

approved