A389109 Decimal expansion of the smallest dihedral angle, in radians, in a gyroelongated pentagonal pyramid (Johnson solid J_11).

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

Offset

1,2

Comments

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

Also a dihedral angle in a pentagonal orthocupolarotunda, metabidiminished icosahedron, tridiminished icosahedron, augmented tridiminished icosahedron, bilunabirotunda and triangular hebesphenorotunda (Johnson solids J_32, J_62, J_63, J_64, J_91 and J_92, respectively).

Links

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

Polytope Wiki, Augmented tridiminished icosahedron.

Polytope Wiki, Bilunabirotunda.

Polytope Wiki, Gyroelongated pentagonal pyramid.

Polytope Wiki, Metabidiminished icosahedron.

Polytope Wiki, Pentagonal orthocupolarotunda.

Polytope Wiki, Triangular hebesphenorotunda.

Polytope Wiki, Tridiminished icosahedron.

Wikipedia Augmented tridiminished icosahedron.

Wikipedia Bilunabirotunda.

Wikipedia Gyroelongated pentagonal pyramid.

Wikipedia Metabidiminished icosahedron.

Wikipedia Pentagonal orthocupolarotunda.

Wikipedia Triangular hebesphenorotunda.

Wikipedia Tridiminished icosahedron.

Index entries for transcendental numbers.

Formula

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

Example

1.7595068575784586890124560918223596144353555653644...

Mathematica

First[RealDigits[ArcCos[-Sqrt[(5 - Sqrt[20])/15]], 10, 100]] (* or *)
First[RealDigits[Min[PolyhedronData["J11", "DihedralAngles"]], 10, 100]]

Prog

(PARI) acos(-sqrt((1-sqrt(.8))/3)) \\ Charles R Greathouse IV, Oct 07 2025

Crossrefs

Cf. A236367 (the other J_11 dihedral angle).

Cf. A179639 (J_11 volume), A179640 (J_11 surface area).

Cf. A010476.

Sequence in context: A195399 A065170 A388380 * A346589 A113816 A358186

Adjacent sequences: A389106 A389107 A389108 * A389110 A389111 A389112

Keyword

nonn,cons,easy

Author

Paolo Xausa, Sep 23 2025

Status

approved