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

Author

Paolo Xausa, Aug 21 2025

Keywords

• nonn
• cons
• easy

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).

Examples

			1.3047162795687363719907812632876451487306158399...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Pentagonal bipyramid.
• Wikipedia, Pentagonal orthobicupola.

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.

Programs

Mathematica

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

Formula

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

Equals 2*A386852.