A387189 Decimal expansion of the smallest dihedral angle, in radians, in a pentagonal bipyramid (Johnson solid J_13).

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

Offset

1,2

Comments

This is the dihedral angle between triangular faces at the edge where the two pyramidal parts of the solid meet.

Also the dihedral angle between triangular faces in a pentagonal orthobicupola (Johnson solid J_30).

Links

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

Wikipedia, Pentagonal bipyramid.

Wikipedia, Pentagonal orthobicupola.

Formula

Equals arccos((4*sqrt(5) - 5)/15) = arccos((A010532 - 5)/15).

Equals 2*A386852.

Example

1.3047162795687363719907812632876451487306158399...

Mathematica

First[RealDigits[ArcCos[(Sqrt[80] - 5)/15], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J13", "DihedralAngles"]], 10, 100]]

Crossrefs

Cf. A236367 (J_13 smallest dihedral angle).

Cf. other J_30 dihedral angles: A105199, A377995, A377996.

Cf. A179641 (J_13 volume), A120011 (J_13 surface area, divided by 10).

Cf. A384624 (J_30 volume), A384625 (J_30 surface area).

Cf. A010532, A386852.

Sequence in context: A190181 A145092 A210878 * A355977 A356581 A367480

Adjacent sequences: A387186 A387187 A387188 * A387190 A387191 A387192

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 21 2025

Status

approved