A387191 Decimal expansion of the second largest dihedral angle, in radians, in an elongated pentagonal rotunda (Johnson solid J_21).

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

Offset: 1

Author

Paolo Xausa, Aug 22 2025

Keywords

• nonn
• cons
• easy
• new

Comments

This is the dihedral angle between a square face and a pentagonal face.

Also one of the dihedral angles in Johnson solids J_40-J_43, J_72-J_75, J_77-J_79 and J_82.

Examples

			2.677945044588987122248387151818288482168632345...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Elongated pentagonal rotunda.

Crossrefs

Cf. other J_21 dihedral angles: A019669, A228824, A344075, A386530.

Cf. A384213 (J_21 volume), A179637 (J_21 surface area - 10).

Cf. A010476, A105199.

Programs

Mathematica

First[RealDigits[Pi/2 + ArcTan[2], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J21", "DihedralAngles"]], 2], 10, 100]]

Formula

Equals Pi/2 + arctan(2) = A019669 + A105199.

Equals arccos(-2*sqrt(5)/5) = arccos(-A010476/5).