A387147 Decimal expansion of the dihedral angle, in radians, between triangular and square faces in an elongated pentagonal pyramid (Johnson solid J_9).

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

Offset: 1

Author

Paolo Xausa, Aug 18 2025

Keywords

• nonn
• cons
• easy

Comments

Also one of the dihedral angles, in radians, in an elongated pentagonal bipyramid, elongated pentagonal cupola, elongated pentagonal orthobicupola, elongated pentagonal gyrobicupola, elongated pentagonal orthocupolarotunda and elongated pentagonal gyrocupolarotunda (Johnson solids J_16, J_20, J_38, J_39, J_40 and J_41, respectively).

Examples

			2.2231544665792648052267123232835740164638926196505...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Elongated pentagonal bipyramid.
• Wikipedia, Elongated pentagonal cupola.
• Wikipedia, Elongated pentagonal gyrobicupola.
• Wikipedia, Elongated pentagonal gyrocupolarotunda.
• Wikipedia, Elongated pentagonal orthobicupola.
• Wikipedia, Elongated pentagonal orthocupolarotunda.
• Wikipedia, Elongated pentagonal pyramid.
• Index entries for transcendental numbers.

Crossrefs

Cf. A384138 (J_9 volume).

Cf. other J_9 dihedral angles: A019669, A228719, A236367.

Cf. A010476.

Programs

Mathematica

First[RealDigits[ArcCos[-Sqrt[(10 - Sqrt[20])/15]], 10, 100]] (* or *)
First[RealDigits[RankedMax[Union[PolyhedronData["J9", "DihedralAngles"]], 2], 10, 100]]

PARI

acos(-sqrt((10 - sqrt(20))/15)) \\ Charles R Greathouse IV, Aug 19 2025

Formula

Equals arccos(-sqrt((10 - 2*sqrt[5])/15)) = arccos(-sqrt((10 - A010476)/15)).