A391145 Decimal expansion of the smallest dihedral angle, in radians, in a disphenocingulum (Johnson solid J_90).

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

Offset

1,2

Links

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

Polytope Wiki, Disphenocingulum.

Wikipedia, Disphenocingulum.

Formula

Equals arccos(c), where c = -0.176980... is the largest negative real root of 16*x^12 + 352*x^11 + 2264*x^10 + 3416*x^9 - 911*x^8 - 2320*x^7 - 1368*x^6 - 2768*x^5 - 440*x^4 + 1280*x^3 + 800*x^2 + 192*x + 16.

Example

1.74871378602598722798456259406830020257739824600...

Mathematica

First[RealDigits[ArcCos[Root[16*#^12 + 352*#^11 + 2264*#^10 + 3416*#^9 - 911*#^8 - 2320*#^7 - 1368*#^6 - 2768*#^5 - 440*#^4 + 1280*#^3 + 800*#^2 + 192*# + 16 &, 6]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J90", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. other J_90 dihedral angles: A391146, A391147, A391148, A391149, A391150, A391151.

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

Sequence in context: A330596 A296427 A092034 * A153042 A330595 A381657

Adjacent sequences: A391142 A391143 A391144 * A391146 A391147 A391148

Keyword

nonn,cons,easy

Author

Paolo Xausa, Dec 05 2025

Status

approved