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

1,1

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).

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.

Formula

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

Example

2.2231544665792648052267123232835740164638926196505...

Mathematica

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

Prog

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

Crossrefs

Cf. A384138 (J_9 volume).

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

Cf. A010476.

Sequence in context: A256071 A248808 A233206 * A014843 A116987 A219838

Adjacent sequences: A387144 A387145 A387146 * A387148 A387149 A387150

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 18 2025

Status

approved